Magnetic microstructures for magnetic resonance imaging

ABSTRACT

The present invention relates to a magnetic resonance structure with a cavity or a reserved space that provides contrast and the additional ability to frequency-shift the spectral signature of the NMR-susceptible nuclei such as water protons by a discrete and controllable characteristic frequency shift that is unique to each MRS design. The invention also relates to nearly uniform solid magnetic resonance T 2 * contrast agents that have a significantly higher magnetic moment compared to similarly-sized existing MRI contrast agents.

CROSS-REFERENCE TO RELATED APPLICATION

This is a continuation-in-part of International Application No.PCT/US2009/041142, filed on Apr. 20, 2009, which claims the benefit ofU.S. Provisional Patent Application No. 61/071,263, filed Apr. 18, 2008,the contents of which are incorporated herein by reference. This alsoclaims the benefit of U.S. Provisional Patent Application No.61/166,610, filed Apr. 3, 2009, the contents of which are herebyincorporated by reference.

FIELD OF INVENTION

The present invention relates to magnetic resonance imaging contrastagents and methods of magnetic resonance imaging. In particular, thepresent invention relates to magnetic resonance structures used asmagnetic resonance imaging contrast agents and multiplexed magneticresonance imaging methods.

BACKGROUND

Biotechnology and biomedical research have benefited from theintroduction of a variety of specialized nanoparticles whosewell-defined, optically distinguishable signatures enable simultaneoustracking of numerous biological indicators. Optically based labels suchas colored fluorophores, multi-spectral semiconductor quantum dots, andmetallic nanoparticles can be used for multifunctional encoding, andbiomolecular sensing and tracking. However, these optically based labelscan probe only so far beneath most surfaces.

Contrast agents used in magnetic resonance may probe far below mosttissue surfaces. Equivalent multiplexing capabilities are largely absentin the field of magnetic resonance imaging (MRI). MRI cell tracking isbased on the magnetically dephased signal from the fluid surroundingcells labeled with many superparamagnetic iron oxide (SPIO)nanoparticles, or dendrimers, or individual micrometer-sized particlesof iron oxide (MPIO). The continuous spatial decay of the externalfields surrounding these magnetizable particles, or any othermagnetizable particles, imposes a continuous range of Larmor frequenciesthat broadens the water hydrogen proton line, obscuring any distinctionbetween different types of magnetic particles that might specificallylabel different types of cells and as a consequence provide only amonochrome contrast. Accordingly, there is a need in the art todistinguish with magnetic resonance (MR) between different cell types,at the single-cell level, for application in cellular biology, and earlydisease detection and diagnosis.

Alternatively, cellular tracking and labeling by strong magneticresonance T₂* agents can also be used for labeling to provide a strongmonochrome contrast to cellular components. T₂* contrast agents such asnanoscale superparamagnetic particles of iron oxide (SPIOs) and theirmicrometer-sized equivalents (MPIOs) can only be used in limited amountsin a cell without compromising its viability and therefore prevented invivo tracking of single cells from becoming routine. Accordingly, thereis a need in the art for an improved contrast agent.

SUMMARY OF THE INVENTION

The present invention is directed to a magnetic resonance contrast agentconsisting essentially of a plurality of disks of uniform size andmagnetic moment, wherein the disks consist essentially of a singlemagnetic material. Each disk may have magnetic moment from about 10⁻¹⁴A·m² to about 10⁻¹¹ A·m² and vary in size by less than about 5% of theaverage size of the plurality of disks. Each disk may also vary inmagnetic moment by less than about 5% of the average magnetic moment ofthe plurality of disks. The magnetic material of the magnetic resonancecontrast agent may comprise a ferromagnetic, paramagnetic,superparamagnetic, magnetic alloy, or a magnetic compound. The magneticresonance contrast agent may further comprises a coating selected froman oxidation barrier, a corrosion barrier, a mechanical strengtheninglayer, a non-toxic coating, a biologically inert coating, a coating tofacilitate common bioconjugation protocols, a cell-specific antibody orligand coating, and combinations thereof. The magnetic resonancecontrast agent may be a disk shape having a disk diameter ranging fromabout 0.5 μm to about 10 μm and a disk thickness ranging from about 0.5μm to about 10 μm.

The present invention is also directed to a method of super-resolutiontracking of a magnetic resonance visualization contrast agent consistingessentially of a plurality of disks, wherein the disks consistessentially of a single magnetic or paramagnetic material. The methodmay comprise (a) distributing the magnetic resonance visualizationcontrast agent within a sample such that each individual disk isspatially separated from all other disks; (b) performing magneticresonance visualization of the sample to obtain an magnetic resonancevisualization image comprising a plurality of voxels, wherein each voxelcomprises a pixel, each pixel having a pixel intensity; (c) analyzingthe magnetic resonance image to locate each pixel that is darker than abackground pixel intensity resulting from a disk somewhere within acorresponding voxel, determining if any of the darkest voxels aresituated in a contiguous group (d) determining the pixel intensity ofthe darkest voxel; assigning the location of the contrast agent to thedarkest voxels in each contiguous group and (e) determining the locationof each disk within its corresponding voxel by comparing the intensityof the voxel in each contiguous group to the intensity of the darkestvoxel in the contiguous group.

The present invention is also directed to a method of non-invasivelymonitoring at least one characteristic of blood flow through a stentdevice situated within a blood vessel of a living subject. The methodmay comprise (a) providing a stent device comprising an MRS, wherein theMRS induces a known NMR shift in a NMR-susceptible nucleus when exposedto an excitatory electromagnetic pulse delivered at a correspondingresonance frequency; (b) situating the stent device within the bloodvessel of the living subject; (b) exposing the stent device to at leastone or more excitatory electromagnetic pulses delivered at thecorresponding resonance frequency to create a volume of spin-labeledblood molecules; (c) obtaining nuclear magnetic resonance data of avolume of blood flowing downstream of the stent device; and, (d)analyzing the magnetic resonance image data to locate the volume ofspin-labeled blood molecules using the known NMR shift. At least onecharacteristic of blood flow of the method may comprise mass flow rate,volume flow rate, and flow speed. In addition, the characteristic ofblood flow may be compared to a baseline characteristic of blood flow todetermine the presence or absence of occlusions within the stent device.The NMR shift of the spin-labeled blood molecules may be compared to abaseline NMR shift to determine if any deformation in the shape of thestent device has occurred and each different NMR shift is assigned adifferent color on a color scale.

The present invention may also be directed to an magnetic resonancecontrast agent comprising a magnetic material forming a reserved spacethat is connected to a near-field volume, wherein the magnetic materialproduces a substantially uniform magnetic field within the reservedspace, and wherein the uniform magnetic field has a magnitude that issubstantially different than a background magnetic field within thenear-field volume.

The present invention may also be directed to a method of using two ormore MRS, wherein each MRS induces a known NMR shift in aNMR-susceptible nucleus when exposed to an excitatory electromagneticpulse delivered at a corresponding resonance frequency, wherein each ofthe known NMR shifts, and each of the corresponding resonancefrequencies are different for each of the two or more MRS. The methodmay comprise (a) distributing the two or more MRS within a sample; (b)exposing the two or more MRS within the sample to excitatoryelectromagnetic pulses delivered at each of the two or morecorresponding resonance frequencies; (c) obtaining nuclear magneticresonance data after each excitatory electromagnetic pulse; and, (d)using the known NMR shifts to determine the identity of each of the twoor more MRS. Each particular MRS of the method may be targeted toward aparticular tissue or cell. The MRS targeted to a particular cell may bebound to the cell at a cell wall or cell membrane.

BRIEF DESCRIPTION OF THE DRAWINGS

Additional features of this invention are provided in the followingdetailed description of various embodiments of the invention withreference to the drawings. Furthermore, the above-discussed and otherattendant advantages of the present invention will become betterunderstood by reference to the detailed description when taken inconjunction with the accompanying drawings, in which:

FIG. 1 is an illustration of an embodiment of a dual-disk magneticresonance structure.

FIG. 2 is a contour graph showing the calculated magnitude of a magneticfield throughout a plane oriented between the disks of an embodiment ofa dual-disk magnetic resonance structure.

FIG. 3 is an illustration of a method of manufacturing magnetic seriesof intermediate structures produced during an embodiment of a method ofmanufacturing magnetic resonance microstructures.

FIG. 4A is an illustration of a method of manufacturing magnetic seriesof intermediate structures produced during another embodiment of amethod of manufacturing magnetic resonance microstructures.

FIG. 4B is an illustration of a method of manufacturing magnetic seriesof intermediate structures produced during yet another embodiment of amethod of manufacturing magnetic resonance microstructures.

FIG. 4C is an illustration of a method of manufacturing magnetic seriesof intermediate structures produced during still another embodiment of amethod of manufacturing magnetic resonance microstructures.

FIG. 5 is an illustration of an embodiment of a magnetic resonanceidentity system.

FIG. 6 is a graph of the calculated particle volume fraction that fallswithin a bandwidth, δω, about the particle's frequency shift, Δω for anembodiment of a magnetic resonance microstructure.

FIG. 7 is a graph of an alternating-gradient magnetometer hysteresiscurve for an embodiment of a dual-disk magnetic resonance structure.

FIG. 8 is a scanning electron micrographs (SEM) image of an embodimentof a dual-disk magnetic resonance structure.

FIG. 9 is a SEM image of another embodiment of a dual-disk magneticresonance structure.

FIG. 10 is another SEM image of yet another embodiment of a dual-diskmagnetic resonance structure.

FIG. 11 is a graph of the z-spectra produced using three embodiments ofthe dual-disk magnetic microstructures.

FIG. 12 is a graph of the Fourier transformed spin-echo signal generatedfrom direct MRI imaging from an embodiment of the dual-disk magneticresonance structures.

FIG. 13 is a graph showing the z-spectra produced by an embodiment ofthe dual disk magnetic resonance structure using difference delays (ΔT),between off-resonant π/2 pulses.

FIG. 14 is a graph showing the z-spectra produced by an embodiment ofthe dual-disk magnetic resonance structure measured at three differentfield-strengths.

FIG. 15 is a graph showing the z-spectra produced by two embodiments ofthe dual-disk magnetic resonance structure having difference disk radii.

FIG. 16 is a graph showing a map of the z-spectra of numerousembodiments of the dual-disk magnetic resonance structures havingdifferent disk thicknesses (h).

FIG. 17A is an image of a high tilt angle SEM showing a square array ofan embodiment of the dual-disk magnetic resonance particle; in whichpart of the particles have filled interior regions.

FIG. 17B is an MRI image of the dual-disk magnetic resonance particlesshown in 17A.

FIG. 18A is an illustration of an embodiment of a hollow cylinderstructure.

FIG. 18B is a graph showing the calculate magnetic field magnitudeprofile in a mid-plane through an embodiment of a hollow cylindermagnetic resonance structure.

FIG. 18C is a graph showing the calculated magnetic field profile in aperpendicularly oriented mid-plane through an embodiment of a hollowcylinder magnetic resonance structure.

FIG. 18D is a graph showing a histogram recording of the estimatedfrequency shifts in the volume surrounding an embodiment of a hollowcylinder magnetic resonance structure.

FIG. 18E is a graph showing the calculated internal volume fraction ofan embodiment of a hollow cylinder magnetic resonance structure fallingwithin a bandwidth δω of a central frequency shift Δω.

FIG. 19A is a graph showing the spectron of numerous embodiments ofhollow cylinder magnetic resonance structures having different length todiameter rating (L/2 ρ).

FIG. 19B is a graph showing the spectra of numerous embodiments ofhollow cylinder magnetic resonance structures having different degreesof wall thickness variation (Δt/t).

FIG. 20A is a drawing that illustrates the geometrical quantities usedin equation X (sputtering equation).

FIG. 20B is a drawing showing the calculated sidewall coatingthicknesses for embodiments of the hollow cylinder magnetic resonancestructure fabricated using cos^(1/2)Θ, cos Θ, and cos²Θ sputterdistributions.

FIGS. 21A-21F are drawings illustrating the intermediate precuts of anembodiment of a fabrication process for hollow cylinder magneticresonance particles.

FIG. 21A is a drawing showing cylindrical photoresist posts atop agold-titanium coated substrate.

FIG. 21B is a drawing of angled copper evaporation onto the cylindricalphotoresist.

FIG. 21C is a drawing showing magnetic material evaporation.

FIG. 21D is a drawing showing ion-milling removal of magnetic materialand local resputtered coating of the photoresist posts.

FIG. 21E is a drawing showing copper and photoresist removal.

FIG. 21F is a drawing showing the release of hollow cylinders magneticresonance structures by gold-etch or ultrasound techniques.

FIG. 22A is an image from a scanning electron micrograph (SEM) offabricated hollow cylinder magnetic resonance structures produced by anembodiment of a fabrication process.

FIG. 22B is an image from a scanning electron micrograph (ρ≈425 nm)showing an embodiment of a hollow cylinder magnetic resonance structurein the absence of an applied magnetic field (top image) and in thepresence of an applied field (bottom image).

FIG. 23A is a graph showing the z-spectra of an embodiment of a hollowcylinder magnetic resonance structure having a radius of 1 μm, a wallthickness of 75 nm.

FIG. 23B is a graph showing the z-spectra of an embodiment of a hollowcylinder magnetic resonance structure having a radius of 1 μm, a wallthickness of 150 nm.

FIG. 23C is a graph showing the z-spectra of an embodiment of a hollowcylinder magnetic resonance structure having a radius of 425 nm, a wallthickness of 40 nm.

FIG. 23D is a graph showing the z-spectra of an embodiment of a hollowcylinder magnetic resonance structure having a radius of 450 nm, a wallthickness of 50 nm.

FIG. 23E is an MRI image of an array of hollow cylinder magneticresonance structure in which a subset of the hollow cylinders is filledin.

FIG. 24A is an image of a gradient-echo MRI showing hypointense T₂*contrast (dark spots) surrounding locations of embodiments of the hollowcylinder magnetic resonance structures.

FIG. 25 is a drawing illustrating another of a stent magnetic resonancestructure.

FIG. 26 is a drawing illustrating another embodiment of a stent magneticresonance structure.

FIG. 27 is a drawing showing a flow tagging application of an embodimentof a hollow cylindrical magnetic resonance structure at two differentflow speeds.

FIGS. 28-31 show experimental results for an embodiment corresponding toFIG. 27.

FIG. 32 is a graph showing the z-spectra of an embodiment of a dual-diskmagnetic resonance structure in which one disk is smaller in radius.

FIG. 33 is a graph showing the z-spectra of an embodiment of a dual-diskmagnetic resonance structure in which one disk is smaller in radius andthicker than the other disk.

FIG. 34 is a graph showing the z-spectra of an embodiment of a dual-diskmagnetic resonance structure in which one disk is offset relative to theother disk in a direction perpendicular to the applied magnetic field.

FIG. 35 is a graph showing the z-spectra of an embodiment of a dual-diskmagnetic resonance structure in which one disk is offset relative to theother disk in a direction parallel to the applied magnetic field.

FIG. 36 is a graph showing the effect of manufacturing variation on thez-spectra of an embodiment of a dual-disk magnetic resonance structure.

FIGS. 37A-37F are drawings illustrating the intermediate steps of anembodiment of a fabrication process for a dual-disk magnetic resonancestructure.

FIG. 38 are drawings illustrating the effect of the radial distance fromthe wafer center on the profiles of evaporated lift-off patterneddeposits during an embodiment of a fabrication process for a dual-diskmagnetic resonance structure.

FIG. 39 is a scanning electron micrograph of a trilayer evaporatednickel-copper-nickel cylindrical stacks resulting from an embodiment ofa fabrication process for a dual-disk magnetic resonance structure.

FIG. 40 is a scanning electron micrograph comparing the sizes of eachdisk in a dual-disk pair resulting from an embodiment of a fabricationprocess for a dual-disk magnetic resonance structure.

FIGS. 41A-41D are a drawings illustrating an embodiment of a fabricationmethod for a solid high magnetic moment T₂* contrast agent.

FIGS. 42A-42B are scanning electron micrographs showing an embodiment ofa solid high magnetic moment T₂* contrast agent.

FIG. 43 is a graph showing the effect of transverse dephasing ontheoretical single voxel signal intensities during magnetic resonanceimaging of a solid high magnetic moment T₂* contrast agent usingspherical voxel geometry.

FIG. 44 is a graph showing the effect of transverse dephasing ontheoretical single voxel signal intensities during magnetic resonanceimaging of a solid high magnetic moment T₂* contrast agent using cubicvoxel geometry.

FIG. 45 is a graph comparing theoretical single voxel signal intensitiesfrom the magnetic resonance image of a solid high magnetic moment T₂*contrast agent with and without image distortion corrections.

FIGS. 46A-46D are simulated gradient echo MRI images of an embodiment ofa solid high magnetic moment T₂* contrast agent made of various magneticmaterials.

FIG. 46A is a simulated gradient echo MRI images taken using 50-μmisotropic resolution and a magnetic field B₀ oriented parallel to theMRI image slices.

FIG. 46B is a simulated gradient echo MRI images taken using 100-μmdiameter contrast agent particles using a magnetic field B₀ orientedparallel to the MRI image slices.

FIG. 46C is a simulated gradient echo MRI images taken using 50-μmisotropic resolution and a magnetic field B₀ oriented perpendicular tothe MRI image slices.

FIG. 46D is a simulated gradient echo MRI images taken using 100-μmisotropic resolution and a magnetic field B₀ oriented perpendicular tothe MRI image slices.

FIG. 46A is a simulated gradient echo MRI images taken using 50-μmisotropic resolution and a magnetic field B₀ oriented parallel to theMRI image slices.

FIGS. 47A-47C are theoretical magnetic resonance images of singlecontrast agent particles comparing the signal intensities of theparticles at different positions within the cubic voxels.

FIG. 47A shows the effect of position within the voxel on the signalintensity predicted for iron contrast agent particles.

FIG. 47B shows the effect of position within the voxel on the signalintensity predicted for nickel contrast agent particles.

FIG. 47C shows the effect of position within the voxel on the signalintensity predicted for iron oxide contrast agent particles.

FIG. 47D shows the positions of the contrast agent particles within thevoxel boundaries simulated in FIGS. 47A-47C.

FIGS. 48A-48F are gradient-echo MRI images of chemically synthesized andmicrofabricated magnetic resonance contrast agents.

FIG. 48A is a gradient-echo MRI image using 50-μm isotropic resolutionof a prior art MPIO contrast particle.

FIG. 48B is a gradient-echo MRI image using 50-μm isotropic resolutionof a microfabricated solid nickel contrast particle.

FIG. 48C is a gradient-echo MRI image using 50-μm isotropic resolutionof a microfabricated solid iron contrast particle.

FIG. 48D is a gradient-echo MRI image using 100-μm isotropic resolutionof a prior art MPIO contrast particle.

FIG. 48E is a gradient-echo MRI image using 100-μm isotropic resolutionof a microfabricated solid nickel contrast particle.

FIG. 48F is a gradient-echo MRI image using 100-μm isotropic resolutionof a microfabricated solid iron particle.

FIGS. 49A-49F are histograms of single-voxel signal intensities fromtheoretical and experimental magnetic resonance images ofmicrofabricated contrast agents normalized to the background signalintensity.

FIG. 49A is a histogram of theoretical single voxel signal intensity fora microfabricated iron contrast agent normalized to the backgroundsignal intensity.

FIG. 49B is a histogram of the experimentally-measured single voxelsignal intensity for a microfabricated iron contrast agent normalized tothe background signal intensity.

FIG. 49C is a histogram of theoretical single voxel signal intensity fora microfabricated nickel contrast agent normalized to the backgroundsignal intensity.

FIG. 49D is a histogram of the experimentally-measured single voxelsignal intensity for a microfabricated nickel contrast agent normalizedto the background signal intensity.

FIG. 49E is a histogram of theoretical single voxel signal intensity fora MPIO contrast agent normalized to the background signal intensity.

FIG. 49F is a histogram of the experimentally-measured single voxelsignal intensity for a MPIO contrast agent normalized to the backgroundsignal intensity.

FIGS. 50A-50F are graphs showing the fractional hypointensity (1-S/S₀)as a function of dipole moment for various isotropic (cubic) resolutionsand echo times.

FIG. 50A is a graph showing the fractional hypointensity (1-S/S₀) as afunction of dipole moment for a 50-μm isotropic resolution and an echotime of 5-ms.

FIG. 50B is a graph showing the fractional hypointensity (1-S/S₀) as afunction of dipole moment for a 100-μm isotropic resolution and an echotime of 5-ms.

FIG. 50C is a graph showing the fractional hypointensity (1-S/S₀) as afunction of dipole moment for a 50-μm isotropic resolution and an echotime of 10-ms.

FIG. 50D is a graph showing the fractional hypointensity (1-S/S₀) as afunction of dipole moment for a 100-μm isotropic resolution and an echotime of 10-ms.

FIG. 50E is a graph showing the fractional hypointensity (1-S/S₀) as afunction of dipole moment for a 50-μm isotropic resolution and an echotime of 20-ms.

FIG. 50F is a graph showing the fractional hypointensity (1-S/S₀) as afunction of dipole moment for a 100-μm isotropic resolution and an echotime of 20-ms.

FIG. 51 is a gradient-echo MRI image of microfabricated iron diskssuspended in agarose.

FIG. 52 is a TEM image of microfabricated single disk contrast agentsattached to the cell membrane of a biological cell.

FIG. 53 is a TEM image of microfabricated single disk contrast agentsincorporated within the cell membrane of a biological cell.

DETAILED DESCRIPTION

The inventors have designed a magnetic resonance structure (MRS) with acavity or reserved space that provides contrast and the additionalability to frequency-shift the spectral signature of the NMR-susceptiblenuclei such as water protons by a discrete and controllablecharacteristic frequency shift that is unique to each MRS design. Thefrequency-shifted spectral signature, which may be engineered bycontrolling the precise geometry of the MRS, may be used in addition tocontrast to provide for identifying individual MRS's in magneticresonance (MR) image data or in any other nuclear magnetic resonancesystem data, and for distinguishing different MRS types/geometries fromone another within these data. The individual magnitudes offrequency-shifting resulting from individual MRS may be associated withan individual color on a color map of the spectral signatures acquiredfrom each location or from each MRS within an MR image, greatlyenhancing the informational content of MR images. Using the MRS ascontrast agents in MR imaging, the resulting MR imaging data may providea color map of the spectral signature shifts, which provides additionalinformation regarding the identities of individual MRS, in addition tothe contrast signals produced by the MRS.

In the reserved space or cavity of the MRS a substantially, spatiallyuniform magnetic field is generated whose strength is significantlydifferent from that of the background field outside the particle. Thereserved space or cavity allows NMR-susceptible nuclei such as waterprotons to diffuse or flow in and out of the reserved space therebyincreasing the volume of fluid frequency-shifted during the repeatedapplication of resonant electromagnetic pulses. This diffusion modulatesthe signal from a volume of fluid many times greater than the volumecontained in the MRS, and this enhancement allows a lower-density ofparticles to be used in order to produce the contrast, in addition tothe color information.

This frequency-shifting signal is produced by the MRS only if the MRS isexposed to a electromagnetic pulse at a specific resonant frequency thatis precisely specified by the particular design of the MRS. If the sameMRS is exposed to a RF pulse with a frequency that is significantlydifferent from the resonance frequency of the MRS, no signal will beproduced. Individual MRS within an ensemble of MRS in a sample, eachhaving a different resonance frequency, may produce a frequency-shiftingsignal when exposed to an RF pulse at its characteristic resonancefrequency with no signal production by the other MRS having differentresonant frequencies in the ensemble.

A group of essentially identical MRS particles having a reserved spaceand being essentially uniform in size and composition may thus shift thefrequency spectra of NMR-susceptible nuclei by the same discrete andcontrollable amount during exposure to resonant electromagnetic pulse.Different groups of MRS particles constructed to shift the frequencyspectra of NMR-susceptible nuclei by different discrete and controllableamounts may be used to perform multiplexed magnetic resonance scanningin which the different frequency spectrum shifts of the different MRSparticles may be encoded as different colors in the resulting magneticresonance image. The MRS may be produced using a technique that resultsin an essentially uniform size and composition of a plurality of MRS.The combination of creating a reserved space with an essentially uniformmagnetic field and a substantially pure composition both in material,shape, and size, allow use of a relatively low detectable concentrationof a magnetic resonance contrast agent in a magnetic resonance scan ascompared to the amount of the MRI contrast agent required in the priorart.

In addition to MRS structures that provide data that may be used forcolor mapping, the inventors have also created nearly uniform solidmagnetic resonance T₂* contrast agents that have a significantly highermagnetic moment compared to similarly-sized existing MRI contrastagents. Top-down fabrication method may be used to produce these solidMRS contrast agents from virtually any material, including materialswith a high saturation magnetic density such as nickel or soft iron. Asa result, the external magnetic fields produced by the solid MRSparticles are significantly stronger than the corresponding fieldsproduced by existing MRI contrast agents such as superparamagnetic ironoxide nanoparticles (SPIO). In fact, these solid magnetic resonancecontrast agents increase visibility several-fold extending itsapplications to areas such as in vivo single-cell tracking studies. Inaddition, both MRS with a cavity/reserved space and the solidparticulate MRS, are dimensionally consistent from particle to particlefacilitating more quantitative image analysis and making possiblesuper-resolution tracking or locating of the position of an individualMRS within a voxel using both the absolute value of the contrast signaland the relative contrast intensities from surrounding voxels. Thus, allMRS designs may be used as conventional T₂* magnetic resonance contrastagents with significantly improved efficacy relative to other T₂*contrast agents. The substantial uniform dimensions of thesecompositions also allow use of minimal detectable concentrations incomparison to the solid magnetic resonance contrast agents required inthe prior art.

The ability to microfabricate both an MRS with a reserved space and asolid MRS from a variety of different, and highly magnetic materialsprovides great advantages because many of the paramagnetic materialscurrently used for MRI contrast agents (for example, Gadoliniumcomplexes) are considered potentially toxic at some threshold amount.The MRS may be used in a number of applications including magneticresonance frequency shifts of water protons and other NMR-susceptiblenuclei for magnetic resonance calibration/testing/fabrication, magneticresonance spatial calibration markers, specificdetection/labeling/tracking of biological cells,distance/pressure/vibration/torque sensors, torque/orientationalmeasurements, magnetic separation, fluid pumps or mixers, localized RFmagnetic heating elements, localized magnetic field gradients,microfluidic applications, flow cytometry, flow sensors for stents, andsingle cell characterization.

A detailed description of embodiments of the MRS, methods of producingan MRS, and methods of using the MRS is provided below.

1. Definitions

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting. As used in thespecification and the appended claims, the singular forms “a,” “an” and“the” include plural referents unless the context clearly dictatesotherwise.

For recitation of numeric ranges herein, each intervening number therebetween with the same degree of precision is explicitly contemplated.For example, for the range of 6-9, the numbers 7 and 8 are contemplatedin addition to 6 and 9, and for the range 6.0-7.0, the numbers 6.0, 6.1,6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9, and 7.0 are explicitlycontemplated.

a. B₀ Magnetic Field

As used herein, a B₀ magnetic field may be a uniform external appliedmagnetic field that possesses a uniform magnitude and uniform directionin the absence of any MRS or other magnetic particles. The B₀ magneticfield may also be referred to as a background magnetic field. In certainapplications, the B₀ magnetic field may be produced by a magneticresonance visualization device such as an MRI scanner.

b. Far-Field Volume

As used herein, the far-field volume may be the region outside thenear-field volume of a MRS that encompasses the far-field magnetic fieldinduced by the MRS structure.

c. Near-Field Volume

As used herein, the near-field volume may be a volume that isessentially centered on a MRS and extends out from the structure to adistance of no more than a few times the maximum spatial dimension ofthe MRS itself. The extent of this near-field volume may scale with thesize of the MRS.

d. Non-Magnetic Material

As used herein, a nonmagnetic material may be a material that does notexhibit a substantial magnetic field either intrinsically or when placedin a magnetizing field. Although nonmagnetic materials are distinguishedfrom ferromagnetic materials and superparamagnetic materials,nonmagnetic materials may not necessarily be completely nonmagnetic innature, but may include materials that are weakly magnetic, very weaklyparamagnetic or diamagnetic in nature. For example, the water that iscommonly detected and imaged in magnetic resonance systems is detectedbecause of the nuclear magnetic resonance of the water. Because themagnetism of the water is extremely weak relative to the magneticmaterials described herein, however, water and the other weakly magneticmaterials described herein may be regarded as nonmagnetic materials.

2. Magnetic Resonance Structures

Provided herein is a magnetic resonance structure (MRS).

a. Solid High Magnetic Moment T₂* Contrast Agents (Solid ParticulateMRS)

The MRS may be a solid particle. The solid particulate MRS may be highmagnetic moment particles for high-resolution imaging in whichindividual particles may be located and tracked with greater precisionfor quantitative analysis. The solid particular MRS may share uniformityfrom one particle to the next. The solid particular MRS may have a highmagnetic moment because each particle uses substantially pure, stronglymagnetic material. The solid particular MRS has these characteristicsbecause it is generated through top-down fabrication as discussed below.

The solid particulate MRS also may share uniformity in shape from oneparticle to the next. The minimum detectable concentration of the solidparticulate MRS when used as a magnetic resonance agent may be as low asan individual solid particulate MRS. The solid particulate MRS may be inthe form of a disk, a cylinder, a pyramid, a cube, a sphere, arectangular block, a rod, a square, a crescent or any shape permutationthereof. The solid particulate MRS may have a uniform shape and surfaceor may have an uneven surface with protractions from the layer.

The solid particulate MRS may be a T₂* contrast agent. The high magneticmoment of the solid particulate MRS may result in a stronger transversedephasing of the water protons around the particle, thus inducing asignificantly higher T₂* contrast relative to existing magnetic particleT₂* contrast agents such as MPIOs of similar size.

Further, the solid particulate MRS may have a very low variability inthe size of the particles or the composition of the material making upthe particle. The size of each individual particles may vary by lessthan 10%, less than 9%, less than 8%, less than 7%, less than 6%, lessthan 5%, less than 4%, less than 3%, less than 2%, and less than 1% ofthe mean size of the particles. As a result, the solid particulate MRSmay be used in an advanced magnetic resonance visualization techniquesuch as super-resolution tracking to a much greater precision forquantitative analysis.

The overall volume of a solid particulate MRS may range from about5×10⁻²² m³ to about 5×10⁻¹⁵ m³, or 5×10⁻²² m³, 5×10⁻²¹ m³, 5×10⁻²⁰ m³,5×10⁻¹⁹ m³, 5×10⁻¹⁸ m³, 5×10⁻¹⁷ m³, 5×10⁻¹⁶ m³, or 5×10⁻¹⁵ m³. Theoverall volume of each solid particulate MRS of a group having aparticular specified size may be consistently the same within about0.1%, about 0.5%, 1.0%, 2.0%, 3.0%, 4.0%, 5.0%, 6.0%, 7.0%, 8.0%, 9.0%,or 10% of the mean volume

In addition, the magnetic moment of the solid particular MRS may beabout 10⁻¹⁵ Am² 10⁻¹⁴ Am², 10⁻¹³ Am², 10⁻¹² Am², 10⁻¹¹ Am² or 10⁻¹⁰ Am².Further, the variation in magnetic moment within a group having aparticular specified magnetic moment may be within about 0.1%, about0.5%, 1.0%, 2.0%, 3.0%, 4.0%, 5.0%, 6.0%, 7.0%, 8.0%, 9.0%, or 10% ofthe mean magnetic moment. The J_(s) values of the solid particulate MRSmay be 0.0 T, 0.1 T, 0.2 T, 0.3 T, 0.4 T, 0.5 T, 0.6 T, 0.7 T, 0.8 T,0.9 T, 1.0 T, 1.1 T, 1.2 T, 1.3 T, 1.4 T, 1.5 T, 1.6 T, 1.7 T, 1.8 T,1.9 T, 2.0 T, 2.1 T, 2.2 T, 2.3 T, 2.4 T, or 2.5 T.

If the solid particulate MRS is a solid disk, the overall diameter ofthe solid disk MRS may range from about 0.5 μm to about 20 μm, or about0.5 μm, 1.0 μm, 2.0 μm, 3.0 μm, 4.0 μm, 5.0 μm, 6.0 μm, 7.0 μm, 8.0 μm,9.0 μm, 10.0 μm, 11.0 μm, 12.0 μm, 13.0 μm, 14.0 μm, 15.0 μm, 16.0 μm,17.0 μm, 18.0 μm, 19.0 μm, or 20.0 μm. The overall thickness of thesolid disk MRS may range from about 0.5 μm to about 20 μm, or about 0.5μm, 1.0 μm, 2.0 μm, 3.0 μm, 4.0 μm, 5.0 μm, 6.0 μm, 7.0 μm, 8.0 μm, 9.0μm, 10.0 μm, 11.0 μm, 12.0 μm, 13.0 μm, 14.0 μm, 15.0 μm, 16.0 μm, 17.0μm, 18.0 μm, 19.0 μm, or 20.0 μm.

The solid particulate MRS may be composed of a non-magnetic layer and/ora magnetic layer or combinations thereof. The thickness of each layermay vary between 1-nm to 1000-nm in thickness or 1-nm, 10-nm, 20-nm,30-nm, 40-nm, 50-nm, 60-nm, 70-nm, 80-nm, 90-nm, 100-nm, 150-nm, 200-nm,250-nm, 300-nm, 350-nm, 400-nm, 450-nm, 500-nm, 550-nm, 600-nm, 650-nm,700-nm, 750-nm, 800-nm, 850-nm, 900-nm, 950-nm, 1000-nm, 1 μm, 2 μm, 3μm, 4 μm, 5 μm, 6 μm, 7 μm, 8 μm, 9 μm, 10 μm, 11 μm, 12 μm, 13 μm, 14μm, 15 μm, 16 μm, 17 μm, 18 μm, 19 μm, or 20 μm. The magnetic materialof the solid particulate MRS may be iron, nickel, chromium, manganese,cobalt, or any magnetic alloy such as permalloy, neodymium alloy,alnico, bismanol, cunife, fernico, heusler alloy, mkm steel, metglas,samarium-cobalt, sendust, or supermalloy. The non-magnetic materialsthat may be used as coatings or to provide cohesion between layers ofthe magnetic materials may be gold, titanium, zinc, silver, tin,aluminum, or any other material that does not generate a magnetic field.The substrate layer used to generate the solid particulate MRS may besilicon, glass, quartz, sapphire, amorphous silicon dioxide,borosilicate or any other inert substance. The photoresistant materialused to generate the solid particulate MRS may be positive/negativephotoresistant material such as a polymethylmethacrylate,polymethylglutarimide, polymers, epoxy-based compounds such as SU-8, andphenol formaldehyde resins such as a mixture of diazonaphthoquinone(DNQ) and novolac resin.

The solid particulate MRS may be in any form and any consistency of thevarious substrates, photoresistant materials, and magnetic materials dueto the photolithographic patterning microfabrication techniquesdiscussed below that allow arrays of many millions of solid particulateMRS that can be simultaneously fabricated. An exemplary solidparticulate MRS is shown in FIG. 40. The solid particulate MRS has a10-nm thick titanium adhesion layer that was evaporated onto asupporting substrate made be silicon, glass, quartz, sapphire, amorphoussilicon dioxide, borosilicate or any other inert substance. A 100-nmlayer of copper is laid over the titanium layer. Blocks of 300-nm thicklayer of iron or nickel surrounded by a 100-nm gold layer are laidacross the copper layer through a bi-layer lift off process describedbelow. Back-sputtered gold ion-milled from the substrate redeposits onthe iron/nickel sidewalls encase the entire solid particulate MRS ofFIG. 41 leaving 100-nm thick top and bottom gold coatings and 50-nmthick gold coatings along the circumferential sidewall of the MRSparticle of FIG. 41. FIG. 42 is a series of SEM images showing theresulting solid particulate MRS.

b. MRS Contrast Agent with a Reserved Space

The MRS may comprise a reserved space. The reserved space may besituated within the interior of the magnetic material or magneticportions of the MRS so as to be at least partially surrounded by themagnetic material or magnetic portions. The near-field volume maycomprise the reserved space. The size of the reserved space may bedependent on the overall size and arrangement of the magnetic materialsin the MRS. The reserved space may be in the form of a disk shape, atubular shape, a spherical shape, or any other geometrical volume solong as the magnetic field formed within the reserved space is anessentially uniform magnetic field.

The MRS may form at least one opening that permits fluid in thenear-field volume to enter and exit the reserved space by diffusion,convection, or directional flow. The reserved space may be the mainregion in which the frequency-shifting of water protons and other NMRsusceptible nuclei occurs. The reserved space may be filled by anon-magnetic fluid.

The magnitude of the frequency shift may be precisely controlled throughvariations in the magnetic strength of magnetic materials used toconstruct the MRS as well as the relative proportions of the dimensionsof the MRS. In general, the magnitude of the frequency shift Δω may beexpressed as:Δw=(γJ _(s)/2)·G  (0)

where γ is the gyromagnetic ratio, J_(s) is the saturation magneticpolarization, and G is a dimensionless ratio of at least two lineardimensions that define the geometry of the MRS. The gyromagnetic ratioand saturation magnetic polarization depend on the NMR-susceptiblenuclei to be frequency-shifted and the choice of magnetic material inthe MRS, respectively. The linear dimensions that define the geometry ofthe MRS are specified by the particular MRS structure and may includedimensions such as length, diameter, wall thickness, and others. Theparticular combination of dimensions that make up G vary between MRSwith different geometries. For example, for a dual-disc MRS, describedin detail below:G=[(S−h/2)((S−h/2)² +R ²)^(1/2)−(S+h/2)((S+h/2)² +R ²)^(1/2)]  (0.1)

where h is the disk thickness, R is the disk radius, and 2S is thecenter-to-center disk separation.

If the MRS structure is a hollow cylinder, also described in detailbelow:G=L·[(L ²+(2ρ+t)²)^(−1/2)−(L ²+(2ρ−t)²)^(−1/2)]  (0.2)

where t is the cylinder wall thickness, 2ρ is the cylinder diameter, andL is the length of the cylinder.

For MRS with other structural geometries, similar dimensionless ratios Gmay be derived using magnetostatic theory. However, because G is adimensionless ratio of at least two or more dimensions, the value of Gis independent of the overall size of the MRS structure. Depending onthe particular dimensions and structure of the MRS, G may vary betweenabout 0.1 and about 2. In various embodiments, G may be about 0.0001,0.0005, 0.0006, 0.0007, 0.0008, 0.0009, 0.001, 0.005, 0.01, 0.02, 0.03,0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.10, 0.11, 0.12, 0.13, 0.14, 0.15,0.16, 0.17, 0.18, 0.19, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, or2.0.

(1) Essentially Uniform Magnetic Field

The magnetic material of the MRS with a reserved space may produce amagnetic field throughout the near-field volume and far-field region. Anessentially uniform magnetic field may be produced in the reserved spaceinside the near-field volume, and a spatially decaying magnetic fieldmay be produced in the volume external to the MRS.

The sharpness and signal strength of the frequency-shifting signalproduced by the MRS depends most directly on the characteristics of theessentially uniform magnetic field within the reserved space of the MRS.In order to induce a detectably distinct characteristic Larmor frequencyin any NMR-susceptible material, such as water protons passing throughthe essentially uniform magnetic field, the magnitude of the essentiallyuniform magnetic field must be sufficiently different from thesurrounding magnetizing field. The magnitude of the essentially uniformmagnetic field may be specified by the selection of magnetic materialsand arrangement of the magnetic materials in the MRS.

The magnetic material of the MRS may be selected to have a particularsaturated magnetic polarization (J_(s)), resulting in an essentiallyuniform magnetic field within the reserved space (MRS field+backgroundfield) that is different in magnitude from the background fieldmagnitude, particularly when the magnetic material is magnetically fullysaturated. However, even when the magnetic material is only partiallymagnetized, the essentially uniform magnetic field may be sufficientlydifferent from the background field if the magnetic material has asufficiently high J_(s). Typically, the magnetic materials of the MRSwill reach fully saturated magnetization within typical background MRfields. The detectable Larmor frequencies induced by the MRS may berelatively insensitive to the magnitude of the applied magnetic field ofdifferent magnetic resonance devices if the magnetic moment or momentsof the MRS are fully saturated by background MR fields.

Alternatively, if the magnetic material selected for the MRS is apermanent magnetic material such as magnetite, the essentially uniformmagnetic field within the reserved space may be significantly differentfrom the background magnetic field even at relatively low (or zero)background magnetic field magnitudes because the MRS generates amagnetic field independently of the background magnetic field.

The magnetic field may be a local region of interest within thenear-field region of the MRS. This region may be where the totalmagnetic field is substantially uniform and substantially different inmagnitude from any background magnetic field. The region of interest inwhich the essentially uniform magnetic field is induced by the MRS maynot be confined to be within the reserved space extending in a regionoutside of the reserved space, but within the near-field region.Alternatively, the essentially uniform magnetic field may not extendthrough the entire reserved space.

The material to which the essentially uniform magnetic field induces acharacteristic Larmor frequency may be any material containing nucleiknown in the art to be susceptible to nuclear magnetic resonance due tothe nuclei containing an odd number of protons or neutrons. Non-limitingexamples of nuclei susceptible to NMR include ¹H, ²H, ³H, ¹³C, ¹⁰B, ¹¹B,¹⁴N, ¹⁵N, ¹⁷O, ¹⁹F, ²³Na, ²⁹Si, ³¹P, ³⁵Cl, ¹¹³Cd, ¹²⁹Xe, and ¹⁹⁵Pt. Thematerial to which the essentially uniform magnetic field induces acharacteristic Larmor frequency may be water containing ¹H protons.

(2) Principle of Operation

The MRS includes a near-field region in which an essentially uniformmagnetic field significantly alters the resonant Larmor frequency of thewater protons or other NMR-susceptible nuclei within the near-fieldregion during exposure of the MRS to a resonant electromagnetic pulse.Magnetic resonance contrast is achieved by measuring the frequency shiftof the near-field water protons and other NMR-susceptible nucleiaffected by the MRS magnetic field during the resonant pulse.

In general, magnetic resonance visualization techniques are based onprocessing an electromagnetic signal originating from water protons orother NMR-susceptible nuclei exposed to an applied magnetic field. Ingeneral, the Larmor precession frequency co of a proton is induced to avalue that is directly proportional to a local magnetic field magnitudeB₀ according, as given in Eqn. (1):ω=−γB ₀  (1)

where γ is the gyromagnetic ratio. The local magnetic field is typicallydominated by the magnetic field applied by the magnetic resonancescanning device. Many existing MRI contrast agents, however, make use ofmagnetic particles such as MPIOs to locally distort the applied magneticfield of the magnetic resonance device to enhance the contrast of theresulting image in a local region surrounding the contrast agent.

A magnetic object induces a magnetic field that continuously decays inmagnitude as a function of the distance from the magnetic object withina relatively extended far-field volume surrounding the magnetic object.In the vicinity of any magnetic structure, proton precession frequenciesvary proportionally to the spatially varying magnetic fields produced bythat structure. Accordingly, NMR spectra integrating overNMR-susceptible proton signals from around that structure wouldtypically integrate over broad frequency ranges, leading to broadenedNMR spectral peaks.

Existing MRI contrast agents that include magnetic particles such asmicroparticles of iron oxide (MPIOs) generate magnetic resonancecontrast by locally altering the longitudinal (T₁) or transverse (T₂ orT₂*) relaxation rates using these far-field effects. Because thefar-field effects of these existing MRI contrast agents involvenon-homogeneous magnetic fields, however, no consistent andwell-defined, quantized, and discrete color shift in the Larmorfrequency of the water protons and other NMR-susceptible nuclei withinthe far-field region may be obtained using these existing MRI contrastagents in the prior art.

To yield instead a distinct frequency-shifted color NMR peak, themagnetic structure geometry of the MRS may be such that it produces afluid-accessible, extended spatial volume over which the combinedmagnetic field from the field of the MRS, together with the appliedmagnetizing background magnetic resonance field B₀, is homogeneous anddistinct in magnitude from the surrounding magnetic fields. By contrast,the various embodiments of the MRS function as multispectral contrastagents by shifting the resonant Larmor precession frequencies of thewater protons and other NMR-susceptible nuclei in a discrete andcontrollable manner when the MRS is exposed to a resonantelectromagnetic pulse.

The MRS described herein may shift the NMR spectra of NMR-susceptiblenuclei such as water protons contained within a reserved space withinthe near-field region of the MRS during exposure to a resonantelectromagnetic pulse. For example, the reserved space may be within amagnetizable shell or between neighboring magnetizable elements. Withinthe reserved space, the MRS may function as a specialized local magneticfield shifter.

The MRS may consist of specially shaped magnetizable elements, which areexemplified by 102 and 194 in FIG. 1. Once magnetized to saturation bythe background magnetic field B₀ (typically at least a few Tesla inmagnitude), the specially shaped magnetizable elements may generatelocalized regions of spatially homogeneous magnetic fields within areserved space, which are exemplified by 110 in FIG. 1. The spatiallyhomogeneous magnetic fields may have a magnitude substantially differentfrom that of any surrounding magnetic fields. Hydrogen protons in thewater molecules or other NMR-susceptible nuclei present in theselocalized homogeneous magnetic field regions may experience a shift inLarmor precession frequency when the MRS is exposed to a resonantelectromagnetic pulse, and the presence of the magnetic resonancestructure may be inferred via detection of these frequency-shifted NMRspectra. Signals originating from one particular type of the MRS may bedifferentiated from other types of MRS by using a type of MRS thatinduces discrete and controllable Larmor precession frequencies duringresonant electromagnetic pulse that are detectably different from theLarmor precession frequencies induced by the background magneticresonance magnetic field and the local magnetic field of the other typesof MRS during electromagnetic pulses at their respective resonantfrequencies.

The spatial profile and homogeneity of the local magnetic field withinthe reserved space may be accurately specified and controlled by theselection of magnetic materials and the size, shape and arrangement ofthe magnetic materials of the MRS. The degree of homogeneity of thelocal magnetic field of the MRS directly influences the sharp definitionof the resulting shifted nuclear magnetic resonance (NMR) peaks. Thespatial extent of the homogeneous magnetic field directly influences themagnitude of the resulting shifted color nuclear magnetic resonance(NMR) peaks. Although the spatial extent of the homogeneous magneticfield is proportional to the physical sizes of the magnetizable elementsof the MRS, the same is not true for the amount of water protons andother NMR-susceptible nuclei that may contribute to thefrequency-shifted signal, due to the additional effect of diffusion.

(3) Effect of Diffusion

The diffusion of fluid into and out of the reserved space within thenear-field region effectively increases the volume of frequency-shiftedwater protons or other NMR-susceptible nuclei by increasing the overallnumber of water protons or other NMR-susceptible nuclei influenced bythe magnetic field within the reserved space. The diffusion effectsignificantly increases the contrast signal strength produced by MRSrelative to a similarly-sized volume of fluid.

In the MRS, the number of water protons or other NMR nuclei that areexposed to the homogeneous field regions within each reserved space isenhanced by the continual random self-diffusion of fluid containingNMR-susceptible nuclei in and out of each reserved space. The enhancedmagnitude of the shifted nuclear magnetic resonance (NMR) peaks due tothese diffusion effects may benefit the MRS regardless of size, and mayespecially benefit from a micrometer or smaller sized MRS.

In the absence of diffusion effects, the effective time for thereplacement of frequency-shifted water protons and other NMR-susceptiblenuclei within the near-field region of a magnetic contrast particle islimited to a length of time on the order of the longitudinal relaxationtime, T₁ (2-3 sec.). The refresh time (τ_(d)) for self-diffusion torefresh the fluid within a reserved space of a magnetic resonancestructure scales with the square of the structure's external dimension(R²). As the size of the MRS is reduced, the saturated magnetization ofNMR-susceptible nuclei falls only linearly with R, rather than inproportion to the structure's volume (R³). Using the diffusivity ofwater (2.3×10⁻⁹ ms⁻²), the distance diffused during the time T₁((6D·T₁)^(1/2)) is about 0.2 mm. Therefore, if the MRS is smaller thanabout 0.2 mm, the diffusivity effect enhances the magnitude of thesaturated magnetization of NMR-susceptible nuclei.

Although diffusion is one mechanism by which water or otherNMR-susceptible nuclei may move in and out of the reserved spaceresulting in enhancement of the frequency-shift signal, NMR-susceptiblenuclei may move in and out of the reserved space due to other mechanismsincluding convection due to the flow of fluid in and out of the reservedspace. The specific mechanism by which NMR-susceptible nuclei aretransported in and out of the reserved space may depend on the specificstructure of the MRS, the specific environment in which the MRS is to beused, and the specific use of the MRS.

(4) Colormetric Frequency-Shifting

The MRS may be designed to frequency-shift water protons or otherNMR-susceptible nuclei by a wide range of discrete and controllableamounts relative to the background frequency-shift of surroundingNMR-susceptible nuclei. This frequency-shift signal of each MRS designmay be used to identify each MRS individually within magnetic resonanceimaging data. At least two MRS may be designed to frequency-shift theNMR-susceptible nuclei by discrete and controlled amounts such that thefrequency-shift of each MRS is distinguishable from the backgroundfrequency-shift as well as the frequency-shift of any of the other MRS.The individual magnitudes of NMR frequency-shifting resulting fromindividual MRS may be associated with an individual color on a color mapof the spectral signatures of the individual voxels within an MR image,greatly enhancing the informational content of MR image data. Thiseffective color signal provides additional information regarding theparticular configuration of the MRS in the nuclear resonance image.

As described in detail elsewhere in this application, thefrequency-shift induced by a particular MRS may be controllably andconsistently specified by a combination of the magnetic materialincluded in the MRS and the shape, dimensions, and separation distancesof the magnetic structures included in the MRS. Using a top-downfabrication process, described in detail below, to produce the MRS,magnetic materials having a wide range of magnetic properties may beformed into highly reproducible MRS configurations with preciselydefined reserved spaces. As a result, the MRS particles may be designedand produced to reliably frequency-shift NMR-susceptible nuclei by anamount that is up to several orders of magnitude higher than anyexisting chemical-shift MRI contrast agent.

The MRS may be designed and produced to frequency-shift aNMR-susceptible nucleus by any amount ranging from about −10 Hz up toabout −10 MHz. Other designs of the MRS may frequency-shift aNMR-susceptible nucleus by about −10 Hz, about −50 Hz, about −100 Hz,about −150 Hz, about −200 Hz, about −400 Hz, about −600 Hz, about −800Hz, about −1 kHz, about −10 kHz, about −20 kHz, about −50 kHz, about−100 kHz, about −200 kHz, about −400 kHz, about −600 kHz, about −800kHz, about −1 MHz, about −2 MHz, about −5 MHz, and about −10 MHz.

Magnetic resonance imaging devices and methods may be used to obtainmultispectral colormetric NMR frequency-shift mapping using eitherdirect imaging methods or indirect imaging methods. Using a directimaging method, a single excitatory electromagnetic pulse at theresonance frequency of each MRS is used to frequency-shift theNMR-susceptible nuclei within the reserved volume, followed by NMRvisualization. In this method, diffusion effects do not enhance thestrength of the NMR signal contrast because the MRS frequency-shift theNMR susceptible nuclei only during the brief time of the excitatoryelectromagnetic pulse. Although the spatial resolution obtained usingdirect imaging is higher due to the concentration of frequency-shiftednuclei to the reserved space, the signal-to-noise ratio is relativelylow.

Indirect imaging methods use a series of temporally separated excitatoryelectromagnetic pulses at the resonance frequency of each MRS followedby NMR visualization of the frequency-shifted nuclei. A significantlylarger volume of NMR-susceptible nuclei such as water protons arefrequency-shifted using this methods since fluid has sufficient time todiffuse in and out of the reserved space between excitatory pulses,effectively replenishing the reserved space with non-frequency shiftednuclei. As a result, the magnitude of the contrast signal issignificantly increased, although the resolution of the signal locationis somewhat degraded due to the diffusion of the frequency-shiftednuclei throughout the near-field region of the MRS and beyond during theseries of excitatory pulses.

(5) Minimum Detectable Concentration

In order for an MRS to be detected, the contrast signal must exceed thebackground noise. In the case of T₂* contrast signaling, the contrastsignal may result from interactions of NMR susceptible nuclei with therapidly decaying magnetic field external to the MRS. In this case, thestrength of the contrast signal may be governed by the magnitude of themagnetic moment produced by the MRS within the background magneticfield. In order to be detected using typical researched levelhigh-resolution magnetic resonance visualization methods, the minimummagnetic moment may be about 10⁻¹⁵ A·m², 10⁻¹⁴ A·m², 10⁻¹³ A·m², 10⁻¹²A·m², 10⁻¹¹ A·m², or 10⁻¹⁰ A·m². This exact required minimum will dependon imaging resolution and background noise levels particular to imagingprotocols and imaging equipment. For low resolution imaging that mayinclude routine clinical low-resolution imaging the minimum magneticmoment may be higher than all these numbers.

The magnetic moment typically depends on the volume of magnetic materialin the MRS as well as the saturated magnetic polarization J_(s) of themagnetic material, a measure of the magnetic strength of the material.As a result, an MRS constructed from a material with a high J_(s), suchas iron, may produce a detectable magnetic moment using a much smallervolume of magnetic material compared to existing magnetic particlecontrast agents, such as MPIOs. For example, if the MRS is a solid diskmade of iron (J_(s)=2.2), a single particle having a diameter of about0.5-μm may produce a suitably high magnetic moment for detection usingtypical high resolution NMR visualization methods.

For MRS having a reserved space, and being used not in the T₂* contrastmode, but in their multispectral frequency shifting mode (describedabove), the contrast signal strength may result from the interactions ofNMR-susceptible nuclei such as water protons within the reserved spaceduring the time that the MRS is exposed to an excitatory electromagneticpulse at the resonance frequency of the MRS. If the MRS is exposed tomultiple excitatory pulses, diffusion effects enhance the volume offrequency-shifted nuclei as described above, resulting in a strongercontrast signal compared to a similarly-sized MRS lacking the diffusioneffects. Consequently, the strength of the signal, which is proportionalto the volume of frequency-shifted nuclei, may be many times greaterthan the volume of the reserved space, thanks to the contribution of thenatural diffusion effects. The contrast signal must exceed thebackground signal levels in order to be detected.

Because the contrast signal strength of a MRS with a reserved spacedepends in part on diffusive effects, the overall size of the MRS is asignificant factor. Ultimately, the minimum useable size of the MRS maynot be limited by fabrication techniques, but by the refresh time(τ_(d)) for self-diffusion. Ideally, fast diffusion helps increase thevolume of water contributing to contrast signal, but the diffusionalexchange of fluid in and out of the reserved space of a magneticresonance structure should not be so fast as to broaden the peak of theNMR signal by more than the shift of the NMR peak relative to the NMRpeak shift. Because the MRS is capable of generating sizeable NMR peakfrequency shifts, the diffusional broadening of the NMR peak becomessignificantly limiting for structures below about 100 nm in size, wherethe magnetic material concentrations required are in the nanomolarregime. The magnitude of the NMR signal, the shift of the NMR signalpeak relative to water protons and other NMR-susceptible nuclei in thefar-field region, and the width of the shift NMR signal peak are alldependent on the materials and geometry of the MRS.

If continual longitudinal relaxation is assumed, the magnetic momentsaturated out of each magnetic resonance structure pulsed over a timet=2T₁ is (m_(pulse)/2)*(T₁/τ_(d))*(1−e⁻²). Because the signal-to-noiseratio (SNR) varies with the voxel volume of the magnetic resonanceimaging device, at least about 1%, 2%, 3%, 4%, 5%, 6%, 7%, 8%, 9%, or10% fractional saturation of the water protons or other NMR-susceptiblenuclei may be needed for reliable detection of an MRS. The minimumdetectable concentration of the MRS with a reserved space may be about10⁻¹⁶ M, 10⁻¹⁵ M, 10⁻¹⁴ M, 10⁻¹³ M, 10⁻¹² M, or 10⁻¹¹ M, depending onthe overall size and magnetic material of the NMR, and the resolutionand background noise of the NMR imaging device. For example, if the MRSwith reserved space is a about 1 micrometer in overall size, the minimumdetectable concentration may be about 10⁻¹⁴ M. In general, smaller sizedMRS will have lower detectable concentrations than larger MRS, due tothe relatively higher contribution of diffusion effects in the smallerstructures. That is, although the required molar concentration(representing a measure of number of individual MRS's) must increase asMRS sizes decrease, the total amount of material required (which is ofcourse less for each smaller MRS) will go down overall, leading to ahighly favorable scaling of required material concentrations and MRSsize decreases. Thanks to diffusion, the required concentration reducesquadratically with the MRS size.

The minimum detectable concentration of the MRS may be well below thatof existing contrast agents such as chemical exchange contrast agents,gadolinium relaxivity-based contrast agents and may be comparable to theminimum detectible concentration of existing SPIO contrast agents.Further, since existing gadolinium and SPIO agents are not spread evenlythroughout the body after administration, the minimum detectableconcentration of the MRS may be far below that of the actual detectedconcentrations of other exiting agents including SPIO contrast agents.

The minimum detectible concentration may also be quantified as theminimum number of contrast particles per unit volume that may bedetected by typical magnetic resonance visualization devices. For allMRS, including solid particulate MRS and MRS including a reserved space,single particles may be detected using typical existing magneticresonance visualization devices such as MRI scanners. As a result, theminimum number of particles that may be detected per unit volume mayoften be as low as one particle per unit volume. The ability to detectsingle particles depends in part on the overall size of the particle, asdiscussed above for both the solid particulate MRS and the MRS with areserved space, in addition to the image resolution of the magneticresonance visualization device. Further, in order to discriminatebetween two or more individual particles the particles may need to havea minimum separation distance. For the case of solid MRS, this minimumwould be at least one imaging voxel. For the case of cavity/reservespace MRS, this minimum can be far smaller that even a single voxelbecause the frequency discrimination can be used to separate the two. Inorder to minimize, however, the signal distortion due to interference ofthe magnetic field of one MRS with a second MRS, the MRS may beseparated by a distance of at least 2-3 times the overall size of theMRS, which will generally still be many times smaller than an individualvoxel size.

c. Geometric Arrangements of Magnetic Material for Reserved Space MRS

The magnetic resonance contrast provided by the reserved space MRS ishighly sensitive to its size and arrangement of the magnetic materials.The magnetic material may form the reserved space within a continuousstructure, or within an arrangement of two or more magnetic portions.The two or more magnetic portions may be separate structures, ordifferent portions of an integral structure. The two or more magneticportions may be formed in any shape and held in any arrangement suchthat an essentially uniform magnetic field is formed within the reservedspace when the MRS is placed in a magnetizing field. The reserved spaceMRS may be any variance or defamation in shape or thickness of the MRS.The reserved space MRS may be a dual disk MRS. The reserved space MRSmay also have a tubular or hollow shape, such as a hollow cylinder, aspherical shell, a rod, an elliptical shell, a shell with multiple smallholes, or any other hollow shell shape. For example, the reserved spaceMRS may be a slightly curved cylinder or may be a disc that has varyingthickness over the contours of the disk.

The magnetic material may form at least one or more openings to allowfluid to freely diffuse and/or flow in and out of the reserved spaceinside the near-field volume. The total surface area occupied by the oneor more openings formed by the magnetic material may range from about0.1% to about 90% of the total outer surface area of the MRS. The one ormore openings may also occupy a total surface area ranging from about0.1%, 0.2%, 0.3%, 0.4%, 0.5%, 0.6%, 0.7%, 0.8%, 0.9%, 1.0%, 1.5%, 2.0%,2.5%, 3.0%, 3.5%, 4.0%, 4.5%, 5.0%, 5.5%, 6.0%, 6.5%, 7.0%, 7.5%, 8.0%,8.5%, 9.0%, 9.5%, 10% to about 20%, from about 15% to about 25%, fromabout 20% to about 30%, from about 25% to about 35%, from about 30% toabout 40%, from about 35% to about 45%, from about 40% to about 50%,from about 45% to about 55%, from about 50% to about 60%, from about 55%to about 65%, from about 60% to about 70%, from about 65% to about 75%,from about 70% to about 80%, from about 75% to about 85%, or from about80% to about 90% of the total outer surface area of the reserved spaceMRS. The total outer surface area of the reserved space MRS is dependenton its' overall size and shape.

The MRS may comprise a reserved space enclosed by a semipermeablematerial to allow fluid to move in and out of the reserved space viadiffusion or convection. The semipermeable material may be anybiological or synthetic semipermeable material known in the art. Thesemipermeable material may allow certain molecules or ions to passthrough by diffusion or facilitate diffusion. The semipermeable membranemay be a phospholipid bilayer, a nanoporous polymer, a microporouspolymer, a cell membrane, a thin film composite membrane, polyimide,cellulose ester membrane, charge mosaic membrane, bipolar membrane,anion exchange membrane, alkali anion exchange membrane, and protonexchange membrane. The MRS may comprise a reserved space that isenclosed by a non-permeable material such as gold or titanium coatingsthereby trapping the fluid inside. For example, the MRS may a completelypackage reserved space for use in microfluidic applications as discussedbelow.

(1) Dual-Disk Magnetic Resonance Structure

The reserved space MRS may be in the form of a dual-disk magneticresonance structure (MRS). The dual-disk MRS may include two disk-shapedmagnetic portions held apart at a fixed distance by one or morenon-magnetic support elements. The open geometry of the dual-disk designmay enhance the accessibility of the reserved space to the diffusiveand/or convective exchange of fluid. The one or more non-magneticsupport elements may be in the form of one or more spacers arrangedbetween the two or more magnetic portions of the MRS, or one or morespacers arranged to be located external to the reserved space betweenthe two or more magnetic portions.

The spacer arranged between two or more magnetic portions may maintainthe reserved space such that the reserved space is open to permit afluid to flow in and out of the reserved space or enclosed area offluid. The spacer may be arranged to partially or completely fill thereserved space between the magnetic portions to prevent the movement offluid in or out of the reserved space. The nonmagnetic material of thespacer may have different properties in different environments,including surrounding pH, temperature, and solution salinity. Theseenvironmentally-dependent properties of the nonmagnetic spacer materialmay be utilized to produce a change in the essentially uniform magneticfield or within the reserved space. These changes produce detectablechanges in the signals produced by the dual-disk MRS during observationwith a magnetic resonance system, or change to block or unblock thereserved space thereby making the reserved space inaccessible oraccessible to fluid.

Each spacer may be formed from a non-magnetic material. The non-magneticmaterial of the spacer may be an internal metal post, a photo-epoxypost, a biocompatible material, hydrogel, or various polymer materials.For example, the nonmagnetic material of the spacers may expand orcontract as a function of temperature. As temperature varies, thespacing between the two or more magnetic portions may increase ordecrease, thereby changing the magnitude of the essentially uniformmagnetic field within the reserved space, resulting in a differentspectral shift of water protons and other NMR-susceptible nuclei duringmagnetic resonance probing. The materials of the spacers may decompose,or disconnect from the magnetic portions, thereby disrupting thearrangement of the magnetic portions and eliminating the internaluniform magnetic field inside the reserved space entirely. The spacingof the disks may be altered in response to various physiological andchemical factors by changing the geometry of the spacer. In addition,the dual-disk MRS may be simply inactivated by disintegration of thespacer element.

The magnetic material of the dual-disk MRS may be iron, nickel, a hybridmaterial, or mixtures thereof. The magnetic disk may be layered withdifferent magnetizable materials such as iron, nickel, chromium,manganese, cobalt, or any magnetic alloy such as permalloy, neodymiumalloy, alnico, bismanol, cunife, fernico, heusler alloy, mkm steel,metglass, samarium-cobalt, sendust, or supermalloy. The magnetic diskmay be coated with non-magnetic materials such as gold, titanium, zinc,silver, tin, aluminum, or any other material that does not generate amagnetic field. These non-magnetic materials may also be used to providea cohesive layer between two other magnetic material layers of the disk.Each of these layers may have a thickness of 1-10 nm, 1-nm, 2-nm, 3-nm,4-nm, 5-nm, 6-nm, 7-nm, 8-nm, 9-nm, 10-nm, 20-nm, 30-nm, 40-nm, 50-nm,60-nm, 70-nm, 80-nm, 90-nm, 100-nm, 150-nm, 200-nm, 250-nm, 300-nm,350-nm, 400-nm, 450-nm, 500-nm, 600-nm, 700-nm, 800-nm, 900-nm, 1000-nm,1-μm, 2-μm, 3-μm, 4-μm, 5-μm, 6-μm, 7-μm, 8-μm, 9-μm, 10-μm, 20-μm,30-μm, 40-μm, 50-μm, 60-μm, 70-μm, 80-μm, 90-μm, 100-μm, 150-μm, 200-μm,250-μm, 300-μm, 350-μm, 400-μm, 450-μm, 500-μm, 550-μm, 600-μm, 650-μm,700-μm, 750-μm, 800-μm, 850-μm, 900-μm, 950-μm, 1000-μm, 1-mm, 2-mm,3-mm, 4-mm, 5-mm, 6-mm, 7-mm, 8-mm, 9-mm, 1-cm, 2-cm, 3-cm, 4-cm, 5-cm,6-cm, 7-cm, 8-cm, 9-cm, or 10-cm.

The magnetic disks may be constructed from materials that are magnetizedby a background magnetic resonance field that is much larger inmagnitude than the essentially uniform magnetic field generated by thedual-disk MRS. Because of the quadrature vector addition of magneticfields, only those components of the essentially uniform magnetic fieldthat are parallel or antiparallel to the background magnetic resonancefield need be substantially uniform and homogeneous. The dual-disk MRSmay also be constructed from a permanent magnetic material and may beused with our without background magnetic field. The entire essentiallyuniform magnetic field of the reserved space may be substantiallyuniform and homogeneous.

The disks of the double disk MRS may have a thickness (h) of 1-nm, 2-nm,3-nm, 4-nm, 5-nm, 6-nm, 7-nm, 8-nm, 9-nm, 10-nm, 20-nm, 30-nm, 40-nm,50-nm, 60-nm, 70-nm, 80-nm, 90-nm, 100-nm, 150-nm, 200-nm, 250-nm,300-nm, 350-nm, 400-nm, 450-nm, 500-nm, 550-nm, 600-nm, 650-nm, 700-nm,750-nm, 800-nm, 850-nm, 900-nm, 950-nm, 1000-nm, 1-μm, 2-μm, 3-μm, 4-μm,5-μm, 6-μm, 7-μm, 8-μm, 9-μm, 10 μm. The radius (R) of the disc may be2-nm, 5-nm, 6-nm, 7-nm, 8-nm, 9-nm, 10-nm, 15-nm, 20-nm, 25-nm, 30-nm,35-nm, 40-nm, 45-nm, 50-nm, 60-nm, 70-nm, 80-nm, 90-nm, 100-nm, 150-nm,200-nm, 250-nm, 300-nm, 350-nm, 400-nm, 450-nm, 500-nm, 550-nm, 600-nm,650-nm, 700-nm, 750-nm, 800-nm, 850-nm, 900-nm, 950-nm, 1000-nm, 1-μm,2-μm, 3-μm, 4-μm, 5-μm, 6-μm, 7-μm, 8-μm, 9-μm, 10-μm, 20-μm, 30-μm,40-μm, 50-μm, 60-μm, 70-μm, 80-μm, 90-μm, 100-μm, 150-μm, 200-μm,250-μm, 300-μm, 350-μm, 400-μm, 450-μm, 500-μm, 550-μm, 600-μm, 650-μm,700-μm, 750-μm, 800-μm, 850-μm, 900-μm, 950-μm, 1000-μm, 1-mm, 2-mm,3-mm, 4-mm, 5-mm, 6-mm, 7-mm, 8-mm, 9-mm, 7-mm, 8-mm, 9-mm, 1-cm, 2-cm,3-cm, 4-cm, 5-cm, 6-cm, 7-cm, 8-cm, 9-cm, 10-cm, 20-cm or 30-cm. Thecenter to center separation (2S) between the dual disks may be 50-nm,60-nm, 70-nm, 80-nm, 90-nm, 100-nm, 150-nm, 200-nm, 250-nm, 300-nm,350-nm, 400-nm, 450-nm, 500-nm, 550-nm, 600-nm, 650-nm, 700-nm, 750-nm,800-nm, 850-nm, 900-nm, 950-nm, 1000-nm, 1-μm, 2-μm, 3-μm, 4-μm, 5-μm,6-μm, 7-μm, 8-μm, 9-μm, 10-μm, 20-μm, 30-μm, 40-μm, 50-μm, 60-μm, 70-μm,80-μm, 90-μm, 100-μm, 150-μm, 200-μm, 250-μm, 300-μm, 350-μm, 400-μm,450-μm, 500-μm, 550-μm, 600-μm, 650-μm, 700-μm, 750-μm, 800-μm, 850-μm,900-jam, 950-μm, 1000-μm, 1-mm, 2-mm, 3-mm, 4-mm, 5-mm, 6-mm, 7-mm,8-mm, 9-mm, 10-mm, 20-mm, 30-mm, 40-mm, 50-mm, or 100-mm. The saturationmagnetic polarization (Js) may be 0, 0.1, 0.2, 0.3 T, 0.4 T. 0.5 T, 0.6T, 0.7 T, 0.8 T, 0.9 T, 1.0 T, 1.5 T, 2.0 T, or 2.5 T.

The double disk MRS may be as shown in FIG. 1. In this embodiment, theMRS 100 includes two magnetic disks 102 and 104—an upper magneticportion 102 and a lower magnetic portion 104 that are arranged at aconstant distance from each other, forming a reserved space 106 betweenthe magnetic portions. The reserved space 106 may be filled with anon-magnetic material, such as a fluid, which may be water, a paste, agel or a gas. The non-magnetic material may flow and/or diffuse throughat least a portion of the reserved space 106. When the magnetic portions102 and 104 are placed within a magnetizing field 108, magnetic moments114 and 116 and associated magnetic fields 110 and 112 are induced. Inthe reserved space 106, the induced magnetic fields 110 and 112 interactto form an essentially uniform magnetic field. This essentially uniformmagnetic field induces the nuclear magnetic moments of any materialpassing through the reserved space 106, such as water molecules or otherNMR-susceptible nuclei, to precess at a characteristic Larmor frequencyif the NMR is exposed to a resonant electromagnetic pulse and if thecombined magnetic field is uniform (background+reserved space). Themagnitude of the essentially uniform field in the reserved space issufficiently different from all surrounding fields such that thecharacteristic Larmor frequency of the NMR-susceptible material passingthrough the reserved space 106 during exposure of the MRS to a resonantelectromagnetic pulse and is detectably different from the Larmorfrequency induced by the background field 108 in the absence of the MRS100. The characteristic Larmor frequency is identifiable with theparticular arrangement and choice of materials making up the MRS 100.

The total magnetic field in the reserved space may be equal to the localmagnetic field (reserved field space and background field) created bythe MRS. The total magnetic field in the reserved space 106 may be equalto the combined local magnetic fields 110 and 112 created by the MRS100, in a case in which the MRS 100 is not embedded in a magnetizingfield 108 while in use. A local region of interest may include thecentral portion of the region between the two spaced magnetic disks,such as the disks shown in FIG. 1. The total magnetic field in thereserved space 106 may be a combination of the local magnetic fieldcreated by the MRS 100 and a portion of a background magnetic field whenthe magnetic resonance structure 100 is embedded in the background fieldduring use. Alternatively, the local region of interest may include thecontrol portion of the region between the two spaced magnetic disks suchas the disks shown in FIG. 1.

FIG. 2 shows the calculated distribution of the magnitude of themagnetic field corresponding to the MRS of FIG. 1. The dual-disk MRSgenerates a highly homogeneous magnetic field over a large volumefraction, as shown in FIG. 2, and the open design helps maximize fluidself-diffusion and/or convection that dramatically increases itssignal-to-noise ratio (SNR) over that of existing closed structure MRIcontrast agents, as discussed above. In addition, the dual-disk MRS isinherently scalable and well-suited to massively parallel wafer-levelmicrofabrication techniques explained in detail below. The discs 102 and104 may be held in position by non-magnetic spacers that may include aninternal metal post (see FIG. 8) or one or more external biocompatiblephoto-epoxy posts (see FIG. 9).

The Larmor frequency shift Δω relative to the Larmor frequency of thewater protons and other NMR-susceptible nuclei located in the far-fieldregion of the MRS may be approximated analytically using the estimatedmagnetic field strength at the center of the dual-disk MRS. Usingelementary magnetostatics analysis, the Larmor frequency shift Δω nearthe center of the reserved area for the MRS including a pair ofmagnetically saturated disks may be determined using the relationshipgiven in Eqn. (2):Δω=(γJ _(s)/2)·[(S−h/2)((S−h/2)² +R ²)^(1/2)−(S+h/2)((S+h/2)² +R²)^(1/2)]  (2)

where γ is the gyromagnetic ratio, h is the disk thickness, R is thedisk radius, 2S is the center-to-center disk separation, and J_(s) isthe saturation magnetic polarization. For thin discs with h<<2S≈R, thisreduces to Eqn. (3):

$\begin{matrix}{{\Delta\;\omega} \approx {{- \gamma}\; J_{s}\frac{h\; R^{2}}{2( {R^{2} + S^{2}} )^{3/2}}}} & (3)\end{matrix}$

The Larmor frequency shift may be specified by modifying any of thequantities specified in Eqn. (3), including J_(s), h, R, S andcombinations thereof. For example, if the disks are constructed of softiron, which has a J_(s) of about 2.2 Tesla, a Larmor frequency shift ofabout −10 MHz may be achieved.

The estimates of Larmor frequency shifting described above implicitlyassume alignment between the disc planes and the applied magnetizingmagnetic resonance field, B₀. Such alignment may be passively maintainedby the inherent magnetic shape anisotropy of the MRS, as shown in FIG.10. For any misalignment angle (θ) between B₀ and the disk planes, theresulting magnetic torques on the discs produce an automaticself-aligning pressure of approximately (h/(R²+S²)^(1/2))(J_(s)²/μ₀)·sin(2θ), equating to a pressure of about 10⁻⁸ to about 10⁻⁶N/μm².By comparison, within cellular cytoplasm, the yield stresses range fromabout 10⁻¹³ to about 10⁻⁹ N/μm².

The relatively high homogeneity of the essentially uniform magneticfield (MRS field+background field) within the reserved space of thedual-disk MRS may suppress the background magnetic resonance signalwhile still saturating out about ⅓ of the volume between the discs viaoff-resonant magnetic resonance excitation pulses with bandwidths ofjust a few percent of the shift of the MRS, as shown in FIG. 6. For anequilibrium B₀-aligned magnetization, M₀, and h<<2S≈R, the magneticmoment of the NMR-susceptible nuclei saturated in a single excitationpulse is m_(pulse)≈M₀πR³/3. Since not all of the fluid within thenear-field region exchanges between consecutive excitation pulses,however, this pre-pulse magnetic saturation volume falls with subsequentpulses. For an inter-pulse delay (τ_(d)) of R²/6D, simulations indicatethat a resulting per-pulse average saturation may be about m_(pulse)/2.The spatial distribution of any single excitatory pulse of saturatedmagnetization at some later time, t>>τ_(d), may be approximated byanalogy to an instantaneous point-source diffusion problem, giving Eqn.(4):M _(s)(r,t)≈(m _(pulse)/2)(4πDt)^(−3/2) exp(−r ²/4Dt)exp(−t/T ₁)  (4)

where the final factor accounts for relaxation back into alignment withB₀, and r measures the distance from the MRS. Within a characteristicdiffusion distance, d≡(D·T₁)^(1/2), a τ_(d)-spaced train of suchexcitatory pulses rapidly (over a time of approximately T₁) asymptotesto a steady-state distribution given by Eqn. (5):M _(s)(r)≈(M ₀/4)(R/r)·e ^(−r/d)  (5)

By integrating Eqn. (5) over a spherical voxel of radius R_(v)>>R withR_(v)<<d, the approximate reduction in magnetization surrounding theparticle may be given by Eqn. (6):M _(s) /M ₀≈0.3R/R _(v)  (6)

Eqn. (6) highlights the diffusion-enabled linear scaling that boosts SNRrelative to the cubic scaling that would result if there was nodiffusion.

For example, although the reserved space of a dual-disk MRS having adimension R=2.5 μm (see FIG. 9) constitutes just 0.003% of the volume ofa 50 μm radius voxel, the structure may saturate the Larmor frequency ofthe water protons or other NMR-susceptible nuclei of a volume of that isabout 2% of the voxel. This thousand-fold larger volume of saturatedwater protons or other NMR-susceptible nuclei surrounding the dual-diskMRS potentially enables the simultaneous single particle imaging andspectral identification (see FIG. 17) without need for specializedsensitive micro-coils. For example, the MRI images shown in FIG. 17 wereobtained using a magnetic resonance scanner with macroscopic surface andsolenoidal RF coils up to several centimeters in diameter.

(2) Hollow Cylinder MRS

The MRS may also be in the form of a hollow cylinder MRS. Although thehollow cylinder MRS differs from the dual-disk MRS, the physical basisbehind the NMR spectral shifting properties of the hollow cylinder MRSmay be conceptualized in a similar manner to the dual-disk MRS. Theessentially uniform magnetic field in the reserved space between the twosuitably spaced magnetized disks possesses the necessary homogeneity toinduce such shifted NMR peaks when exposed to a resonant electromagneticpulse. In such a double-disk structure, the disks are assumed alignedsuch that the B₀ magnetic field vector is parallel to the plane of thedisks. However, this alignment requirement restricts orientation onlyabout a single axis; the dual-disk structure is free to rotate about acentral axis parallel to B₀. Because the resulting NMR color frequencyshifts are invariant with respect to this rotation, a variety ofalternative structures, each composed of what may be regarded assuperpositions of rotated dual-disk structures, may also possess theappropriate homogeneous field profiles. Although a hollow cylinderrepresents a surface of revolution of a radially-offset thin rectangle,rather than a disk shape, the similarity of the hollow cylinderstructure MRS to a rotated dual-disk MRS means that the magnetic fieldsin the reserved space may likewise generate distinct spectrally shiftedcolor NMR peaks.

The hollow cylinder MRS may be scalable down to the nano-regime with anoptimal length-to-diameter ratio just above unity. The hollow cylinderMRS is defined by the overall saturation magnetic polarization (Js),wall thickness (t), diameter (2ρ), and length (L). The wall thickness(t) of the hollow cylinder MRS may be 1-nm, 2-nm, 3-nm, 4-nm, 5-nm,6-nm, 7-nm, 8-nm, 9-nm, 10-nm, 15-nm, 20-nm, 25-nm, 30-nm, 35-nm, 40-nm,45-nm, 50-nm, 55-nm, 60-nm, 65-nm, 70-nm, 75-nm, 80-nm, 85-nm, 90-nm,95-nm, 100-nm, 110-nm, 120-nm, 130-nm, 140-nm, 150-nm, 160-nm, 170-nm,180-nm, 190-nm, 200-nm, 250-nm, 300-nm, 350-nm, 400-nm, 450 nm, and500-nm, 550-nm, 600-nm, 650-nm, 700-nm, 750-nm, 800-nm, 850-nm, 900-nm,950-nm, 1000-nm, 2-μm, 3-μm, 4-μm, 5-μm, 10-μm, 100-μm, 200-μm, 300-μm,400-μm, 500-μm, 600-μm, 700-μm, 800-μm, 900-μm, or 1 mm. The diameter(2ρ) may be 50-nm, 100-nm, 150-nm, 200-nm, 250-nm, 300-nm, 350-nm,400-nm, 450-nm, 500-nm, 550-nm, 600-nm, 650-nm, 700-nm, 750-nm, 800-nm,850-nm, 900-nm, 950-nm, 1000-nm, 2-μm, 3-μm, 4-μm, and 5-μm, 10-μm,100-μm, 200-μm, 300-μm, 400-μm, 500-μm, 600-μm, 700-μm, 800-μm, 900-μm,1 mm, 2 mm, 3 mm, 4 mm, 5 mm, 10 mm, 20 mm, 30 mm, 40 mm, 50 mm, 60 mm,70 mm, 80 mm, 90 mm, 1 cm, 2 cm, 3 cm, 4 cm, 5 cm, and 10 cm. The lengthof the hollow cylinder MRS may be 50-nm, 100-nm, 150-nm, 200-nm, 250-nm,300-nm, 350-nm, 400-nm, 450-nm, 500-nm, 550-nm, 600-nm, 650-nm, 700-nm,750-nm, 800-nm, 850-nm, 900-nm, 950-nm, 1000-nm, 2-μm, 3-μm, 4-μm, 5-μm,10-μm, 100-μm, 200-μm, 300-μm, 400-μm, 500-μm, 600-μm, 700-μm, 800-μm,900-μm, 1 mm, 2 mm, 3 mm, 4 mm, 5 mm, 10 mm, 20 mm, 30 mm, 40 mm, 50 mm,60 mm, 70 mm, 80 mm, 90 mm, 1 cm, 2 cm, 3 cm, 4 cm, 5 cm, and 10 cm. Theoverall magnetic polarization (Js) may be 0, 0.1, 0.2, 0.3 T, 0.4 T. 0.5T, 0.6 T, 0.7 T, 0.8 T, 0.9 T, 1.0 T, 1.5 T, 2.0 T, or 2.5 T.

Apart from the smaller nanostructures affording increased biologicalcompatibility, relative to their size, smaller shells may amplifysignals to a larger degree than can larger shells. This signal gain withstructure miniaturization is due to fluid self-diffusion and/orconvection. The effect of diffusion, over typical proton relaxationperiods, becomes appreciable on the micro- and nano-scales. The signalamplification of the hollow cylinder structures are enabled throughmagnetization transfer techniques that exploit the continual exchange offluid between inside and outside the cylindrical shells. The smaller thecylinder structure, the more rapid the fluid exchange. As such, forcomparable total quantities of magnetic material used to construct anensemble of cylindrical shells, an ensemble containing a greater numberof smaller shells can interact with a larger volume of fluid than can anensemble comprising a smaller number of larger shells. Provided thediffusional exchange is not so fast as to frequency-broaden the spectralpeak by more than its shift, the frequency-shifting signals may increasequadratically as the size of the cylindrical structures shrink.

The hollow cylinder MRS shares many of the advantages of the dual-diskMRS, including large, continuously tunable spectral ranges that do notdepend on B₀ for typical magnetic resonance scanners, as well asrelatively low concentration requirements. Additionally, like thedouble-disk MRS, the hollow cylinder may function as a localphysiological probe. For example, if the hollow cylinder MRS was blockedby some substance designed to break down under certain physiologicalconditions, then the hollow cylinder could act as a sensor, with thespectral signal of the MRS turned on or off depending on whetherinternal regions of the MRS were opened or closed to the surroundingfluid as suggested in FIG. 23E. While the hollow cylinder MRS may not bepotentially dynamically adjustable like the double-disk MRS, since thedouble-disk MRS has disk spacing that is determined by separate posts,the single-element construction of the hollow cylinder MRS is simpler,and fabricating the hollow cylinder MRS is more scalable to thenano-regime.

The MRS may be a hollow cylinder MRS 1800, shown in FIG. 18A. The hollowcylinder MRS may function as both a conventional T₂* contrast agent andas a Larmor frequency-shifting contrast agent. The hollow cylinder MRS1800 in this embodiment are formed from shells 1802 of magnetizablematerial of as little as a few nanometers in thickness. In addition tomodulating local magnetic resonance relaxivities like any other magneticparticle, the hollow cylinder MRS 1800 may also induce controlled,tunable nuclear magnetic resonance (NMR) shifts in the surrounding waterprotons and other NMR-susceptible nuclei when the MRS is exposed to aresonant electromagnetic pulse through precise control of the shellheights, radii and wall thicknesses.

FIGS. 18B and 18C illustrate the a schematic illustration of thenumerically calculated magnetic field magnitude profiles of acylindrical shell magnetized to saturation by an applied magnetizationfield B₀ in a longitudinal and cross-sectional plane respectively,demonstrating the hollow cylinder's homogeneous internal magnetic field.FIG. 18E illustrates the distinct, detectable, and controllablefrequency shift of water protons and other NMR-susceptible nucleiinduced by the essentially uniform magnetic field in the reserved spaceof the hollow cylinder structures when the MRS is exposed to a resonantelectromagnetic pulse. The histogram shown in FIG. 18E summarizes thecalculated magnetic field magnitudes (or equivalently, Larmor precessionfrequencies) throughout the space around the hollow cylindrical MRS. Byshowing the relative volumes of space corresponding to each precessionfrequency, or field magnitude, the histogram approximates the resultingNMR spectrum from NMR-susceptible nuclei in the shell's vicinity. Theshifted spectral peak evident in the histogram is due to the shell'sinternal homogeneous field region whose spatial extent is delineated bythe surface contour plot of FIG. 18E.

The shifted resonance line width is influenced largely by theessentially uniform magnetic field homogeneity, which depends on thecylindrical shell geometry as shown in FIGS. 19A and 19B. Although thecylindrical shell walls may have high aspect ratios, the overallcylindrical shell is fairly short, with an optimal length-to-diameterratio just above unity, as shown in FIG. 19B.

For such a hollow cylindrical structure, the NMR frequency shift (Δω) ofthe water protons and other NMR-susceptible nuclei within the reservedspace may be analytically approximated from the magnetic field at thecylinder's center. Assuming a magnetically saturated cylindrical shellof material, the NMR frequency shift near the center of the reservedspace may be expressed as:Δω=γJ _(s) L[(L ²+(2ρ+t)²)^(−1/2)−(L ²+(2ρ−t)²)^(−1/2)]  (7)

where J_(s) is the saturation magnetic polarization, t is the cylinderwall thickness, 2ρ is the cylinder diameter, L is the length of thecylinder. Simplifying Eqn. (7) to a thin-walled structure in whicht«L≈2ρ results in Eqn. (8):

$\begin{matrix}{{\Delta\;\omega} \approx {{- 4}\gamma\; J_{s}\frac{L\;\rho\; t}{( {L^{2} + {4\rho^{2}}} )^{3/2}}}} & (8)\end{matrix}$

The relationship specified by Eqn. (8) indicates that the frequencyshifts of the hollow cylinder MRS may be engineered by varying thecylindrical shell lengths, radii, wall thicknesses, and materialcompositions. In this way, the different spectral signatures ofdifferent cylindrical shells may be regarded as magnetic resonancefrequency analogs to the different optical colors of different quantumdots. However, the geometry of the cylindrical structure, rather thandot size, determines the spectral response of the cylindrical shell.Because the geometrical parameters of the cylindrical structure arecombined into a dimensionless ratio in Eqn. (8), the color magneticresonance frequency shifts are controlled specifically by structuregeometry, but are independent of the overall size of the cylindricalstructure. Provided that all dimensions of the cylindrical structuresare scaled proportionally, nanoscale shells are capable of shifting thecolor NMR frequencies of the surrounding water protons and otherNMR-susceptible nuclei by a similar amount to comparably-proportioned,but far larger cylindrical structures. Because the amount offrequency-shifting Δω is proportional to a dimensionless ratio oflengths used to specify the MRS geometry, the magnitude of Δω isindependent of the overall size of the MRS. For example, a larger MRSmay have a lower Δω than a smaller MRS having a different dimensionlessratio of lengths used to specify the MRS geometry.

d. Permanent Magnetic Materials/Magnetizable Materials

The magnetic material used to construct the MRS may be any magnetic ormagnetizable material known in the art. The magnetic material may be apermanent magnetic material or magnetizable material.

The magnetizable material may be a ferromagnetic, paramagnetic orsuperparamagnetic material, an alloy or compound, or a combinationthereof, optionally in combination with a nonmagnetic or weakly magneticfiller material. The magnetic material may be nickel, iron, chromium,cobalt, manganese, various forms of iron oxide, iron nitride variousforms of permalloy, various forms of mu-metal, magnetic alloy such aspermalloy, neodymium alloy, alnico, bismanol, cunife, fernico, heusleralloy, mkm steel, metglas, samarium-cobalt, sendust, or supermalloy or acombination thereof. The magnetic material may be of essentially 100%purity, or may be combined with another material to form a hybridelement. For example, the MRS may be constructed from 100% nickel.

The magnetic material may be selected to produce a substantial magneticmoment either intrinsically or when placed into a magnetizing field. Themagnetic material may have a saturated magnetic polarization (J_(s))ranging from 0 T to about 2 T, and may have a J_(s) of 0, 0.1, 0.2, 0.3,0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7,1.8, 1.9, 2.0 T, 2.1 T, 2.2 T, 2.3 T, 2.4 T, or 2.5 T. For example, themagnetic material included in the MRS may be soft iron with a J_(s)=2.2T The magnetic material may also be nickel with a J_(s) ranging fromabout 0.5 T to about 0.6 T. The magnetic material may be iron oxide witha J_(s)=0.5 T. The magnetic material may also have a magnetic momentthat is saturated when the magnetic material is placed in magnetizingfields having strength within the operating capacity of a magneticresonance visualization system.

The magnetic material may be a single magnetic material, or acombination of two or more magnetic materials. The combination of two ormore magnetic materials may be in the form of an alloy in which themagnetic materials are combined in a homogenous mixture, or in the formof a layered magnetic structure in which two or more magnetic materialsare formed into two or more discrete layers. Each layer may be made upof a different magnetic material than an adjoining layer.

e. Hybrid Materials and Nonmagnetic Materials

The non-magnetic materials, or hybrid materials containing a mixture ofone or more magnetic and non-magnetic materials may be used to constructthe MRS in addition to the magnetic materials. These non-magnetic orhybrid materials may be used to position the magnetic materials in aspatial arrangement suitable for forming a reserved space, to modify thediffusion and or flow of fluids in and out of the reserved space, toreinforce the strength of the magnetic materials, and to impartdesirable surface properties to the MRS such as biocompatibility,cell-specific affinity, or hydrophobicity. Further, magnetic materialsmay be deliberately mixed with non-magnetic materials in order to modifythe magnetic properties of the resulting mixture. The non-magneticmaterials may include non-magnetic metals such as copper, titanium, andgold. In addition, the non-magnetic materials may include non-metalssuch as a ceramic, a plastic, or a photoresist material. Thenon-magnetic materials may be physically separate from the magneticmaterials, or the non-magnetic materials may be mixed or interspersedamong the magnetic materials in the form of particles or layers to formthe hybrid material.

The hybrid material may include two or more alternating magnetic andnon-magnetic layers, and/or a conglomeration containing smallerparticles of magnetic material embedded within a host non-magneticmaterial. The hybrid element may be a magnetic material and/or layeredmagnetic structure with an outer coating made of a non-magneticmaterial. The non-magnetic coating may be an oxidation or corrosionbarrier, a mechanical strengthening layer, a non-toxic coating, abiologically inert coating such as titanium, or a coating to facilitatecommon bioconjugation protocols such as gold. The gold coating may befurther functionalized using a technique such as thiol-based chemistry.In addition, the non-magnetic coating may include a coating applied toact as a non-magnetic buffer zone to inhibit magnetic clumping ofmultiple MRS particles, to improve field uniformity by physicallyexcluding access to select surrounding spatial volumes over which fieldsmight be less uniform than desired, to vary the hydrophobicity of theMRS to enhance or diminish fluid flow through the MRS, or to target theMRS to a specific site or cell by coating the MRS with a particularantibody or other ligand.

f. Overall Size of MRS

The size of the MRS may depend on the intended use of the MRS. Theoverall size of the magnetic resonance structure (MRS) may range fromabout 10 nm to about 5 cm, and may be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20,30, 40, 50, 60, 70, 80, 90, 100, 100, 200, 300, 400, 500, 600, 700, 800,900 or 1000 nm, or 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70,80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, or 1000 μm, or 2,3, 4, 5, 6, 7, 8, 9, or 10 mm, or 2, 3, 4, or 5 cm. The size of the MRSmay be selected according to its particular application or use. Inapplications such as blood flow visualization or perfusion imaging, theMRS may range in size from about 1 mm to about 5 cm. The size of the MRSmay be matched with the size scale of a particular blood vessel. Forexample, the upper size limit of the MRS may match the size of a humanaorta. The MRS may also be larger for use in applications such asindustrial flow visualization.

The MRS may also have a maximum dimension between about 10 nm and about100 μm. The MRS may be smaller than about 10 nm to approach molecularsize, and may be particularly useful in micro-tagging applications. TheMRS may also have a maximum dimension ranging from about 50 nm to about10 μm, which may facilitate cellular uptake in a biological, diagnosticand/or medical application.

g. Activatable MRS

The MRS may be used as a “smart” indicator by disrupting the diffusionor flow of fluid into and out of the reserved space using an additionalexternal coating or by filling in the reserved space with a material. Bypreventing the access of fluid into the reserved space, thefrequency-shifting function of the MRS is effectively inactivated. Theexternal coatings or filler materials may be selected to disintegrateunder selected conditions in order to activate the frequency-shiftingfunction of the MRS. Once the external coatings or filler havedisintegrated, the frequency-shifting function of the MRS isirreversibly activated.

The specific structure of the dual-disk MRS may be used as a “smart”indicator by selecting a material for the spacer between the disks thateither disintegrates, swells, and/or shrinks in response to changes inenvironmental factors such as temperature, pressure, pH, salinity,presence of an enzyme, and others. If the spacer material disintegrates,the dual disks are separated and the frequency-shifting function isirreversibly disabled. If the spacer material, which may be a hydrogel,swells or shrinks in response to an environmental factor, the spacingbetween the disks is altered, resulting in an altered magnitude offrequency shift, due to the dependence of the magnitude of the frequencyshift on the relative positioning and dimensions of the magneticelements of the dual-disk MRS, including the disk spacing. Thus, adual-disk MRS having a swellable spacer material produces a frequencyshift that reversibly changes to reflect changes in an environmentalfactor.

A spectrally distinct physiological “smart” indicator may also be formedby either encapsulating the MRS, or filling its reserved spaces, toinhibit internal diffusion or flow (as shown in FIGS. 17 and 23E), whileleaving the far-field spatially trackable image-dephasing capabilitiesunaffected. In the encapsulated MRS, the frequency-shifted signal wouldbe limited to the signal produced by any NMR susceptible nucleiencapsulated within the reserved space of the MRS. If thediffusion-inhibiting or convection-inhibiting material is chosen to bevulnerable to specific enzymatic attack, or to dissolution beyond acertain temperature or pH, subsequent fluid diffusion or convectioncould effectively and irreversibly “turn on” their spectral signals.

h. Far-Field Contrast Characteristics (T₂* Contrast Agents)

The MRS simultaneously provides frequency-shifted magnetic resonancecontrast, as well as a more conventional T₂* contrast function, byvirtue of the magnetic field generated by the magnetic materials of theMRS at relatively far distances from the MRS in the far-field region.The T₂* contrast may be superior to comparably-sized existing MRIcontrast agents since the MRS may be constructed by using a top-downmicrofabrication method that is compatible with using high magneticmoment materials.

Although the magnetic fields induced by the MRS in the near-field regionmay be essentially uniform, the external magnetic fields in thefar-field region exhibit rapid spatial decays in magnitude that manifestthemselves as frequency-broadened, but unshifted, background signalsseen in measured experimental spectra (for example, see FIGS. 11G-11J,12-15, 18D). This broadening is due to the transverse magnetizationdephasing caused by the spatially varying external magnetic fields,resulting in a shortened T₂*. Therefore, the MRS, like any othermagnetic particle, may function as a T₂* contrast agent.

An MRI image of an agarose imaging phantom marked with the hollowcylindrical MRS, shown in FIG. 24, identifies the spatial locations ofthe structures as darkened spots that are similar in appearance to theT₂* contrast spots of existing superparamagnetic iron oxide (SPIO)nanoparticle contrast agents. This SPIO-like contrast is not surprisinggiven that when imaged at typical magnetic resonance spatialresolutions, which exceed nanostructure sizes by orders of magnitude, ahollow shell and a solid particle present similar dipolar external fieldprofiles, and T₂* contrast depends only on magnetic moment. A comparisonof the MRI image of FIG. 24 with MRI images of similarly-sized solidmagnetic particle contrast agents suggests that the contrast fromindividual MRS may be resolved within the typical resolution of magneticresonance images, and that many of the dark spots shown in FIG. 24 arethe contrast from individual MRS. The MRS may therefore function as botha spatial and spectral magnetic resonance contrast agent with magneticdipolar magnetic fields providing spatial contrast in the far-fieldregion and essentially uniform magnetic fields within the reserved spaceproviding spectral contrast within the near-field region.

i. MRS Medium

The MRS generates contrast by frequency shifting the water protons andother NMR-susceptible nuclei within a fluid medium. The fluid medium maybe explicitly included as a part of the MRS. The MRS may additionallyinclude a medium in which one or more of the MRS is dispersed.Non-limiting examples of a medium include a nonmagnetic fluid or anon-magnetic gel. The MRS may be dispersed in a fluid medium such aswater.

3. Method of Making MRS

The MRS may be fabricated using any known method. Because of the strongdependence of the frequency-shifting behavior of the MRS on itsgeometry, the fabrication methods used to produce the MRS by necessitymust inherently produce a MRS with very low variation in MRS geometry orcomposition. Further, in order to produce a consistent frequency shiftbetween individual MRS, the fabrication methods should consistentlyproduce MRS with little variation from individual MRS to MRS.

The MRS may be produced using top-down methods and bottom-up methods.Although the top-down methods produce the MRS, with typically accuratestructural definition and low inter-structural variability, top-downmethods may be more expensive and equipment intensive to implement.Bottom-up methods may be less expensive and equipment-intensive thantop-down methods, but produce the MRS with a relatively higherinter-structural variability. Further, the bottom-up fabrication methodsmay be compatible with a more limited range of materials compared totop-down methods.

Particle complexes can be surface micromachined in various differentways that may, for example, include various combinations of metalevaporation, sputtering, electroplating depositions, and variouslithographic processes together with various wet and dry etchingprocesses.

In order to generate the essentially uniform magnetic fields used toinduce the detectable and consistent frequency shifts of the MRS, thegeometry of the MRS is defined as a relatively exact shape. As a result,the fabrication methods used to produce the MRS must satisfy relativelystringent conditions on the structure geometry in order to producemagnetic structures with highly consistent size and composition.Moreover, for any embodiment in which an ensemble of the MRS is used,the level of inter-particle variability may be reduced to avoid anysubstantial broadening of the overall spectral signal from the ensemble.

a. Top-Down Fabrication

The MRS may be produced using a top-down fabrication method. Thetop-down fabrication method may include at least one spatial patterningstep in the process. The advantages of using top-down fabricationmethods to produce the MRS may include more directly engineeredproperties and increased functionality. Top-down fabrication, such aslithographic techniques, may be used to produce MRS with high materialpurity and low variation in MRS geometry, resulting in highly consistentfrequency-shifting behavior from among individual MRS.

The top-down fabrication method may be a micromachining ormicrofabrication method, which may fabricate a structure having a sizescale on the order of micrometers or less on a substrate. The top-downfabrication method may also be a nanofabrication technique. The MRS maybe produced by the spatial patterning of a layer or layers of materialon the substrate using a technique such as a lithographic technique. Thelithographic technique may be photolithography, electron beamlithography, other charged particle beam lithography, deep-UVlithography, extreme-UV lithography, and x-ray lithography. Othernon-limiting examples of microfabrication techniques include metalevaporation, ion-milling, sputtering, micro-imprinting andnano-imprinting, electroplating, and wet and dry etching. Themicrofabrication method may be used to fabricate structures ranging inoverall size as defined above.

The top-down method may be a resputtering technique used onphotolithographically prepatterned substrates. Often regarded as anundesirable by-product of ion milling, the controlled local redepositionof back-sputtered material may be exploited to yield scalable,large-area, parallel fabrication of accurately defined free-standingnanostructures.

As a result of being made by the top-down fabrication method, the MRSmay possess low cross-structural variation in size or composition. Anygeometrical or compositional variation from structure to structure mayinduce unintended frequency shifts from one structure to the next. Theseunintended frequency shifts may further cause a broadening and degradingof the NMR spectral peaks from signals integrated over ensembles of MRS.

(1) Top-Down Fabrication of Dual-Disk MRS

The dual-disk MRS may be fabricated using any one of at least severaltop-down fabrication techniques. FIG. 3 is a schematic illustration ofan exemplary embodiment of a top-down fabrication method for theproduction of the dual-disk MRS. In this embodiment, titanium and goldlayers are evaporated onto a wafer substrate and a nickel/copper/nickelsandwich layer may be either electroplated or evaporated on top of thegold layer at step 1. A permanent mask layer is formed on top of theouter nickel layer by spincoating, patterning, exposing, developing, andhardbaking a photoresist material at step 2. The top nickel layer and anupper fraction of the copper layer are ion milled through at step 3. Thecopper layer is then wet-etched down to the bottom nickel layer, butstopped before etching through the central copper support at steps 4.Photoresist is spincoated around the sides of the structures at step 5.The top nickel layer is used as a photomask so that subsequentphotoresist flood exposure and development leaves photoresist remainingonly between the nickel layers. The spincoating at step 5 protects thetop nickel layer and patterns the bottom nickel layer for etching. Thebase nickel layer is wet etched and the internal photoresist is removedat step 6. The external support posts, made of SU8 epoxy, arephotopatterned at step 7, and the remaining copper between the nickellayers is wet etched away at step 8.

FIG. 4A is a schematic illustration of another embodiment of a top-downfabrication method used to produce an array of dual-disk MRS. In thisembodiment, titanium and gold are evaporated onto a wafer substrate atstep 1. A thick layer of photoresist is spincoated and patterned at step2. Successive layers of nickel, copper, and nickel are electroplatedinto the photoresist mold at step 3. The photoresist mold is dissolvedat step 4. A copper wet etch is initiated at step 5, and stopped in timeto leave a central copper post at step 6.

FIG. 4B is a schematic illustration of yet another embodiment of atop-down fabrication method used to produce an array of dual-disk MRS.In this embodiment, titanium and gold are evaporated onto a wafersubstrate and successive layers of nickel, copper, and nickel areelectroplated or evaporated onto the substrate at step 1. A permanentmask layer is formed by spincoating, patterning, exposing, developing,and hardbaking photoresist at step 2. The top nickel layer, copperlayer, and base nickel layer are ion-milled through followed by anangled ion-milling to remove redeposited or resputtered material on thestructure side walls at step 3. The copper layer is wet etchedpartially, leaving a central post support at step 4. If externalsupports are desired, SU8 epoxy support posts may be photopatterned atstep 5 and the remaining copper may be wet-etched away at step 6.

FIG. 4C is a schematic illustration of still another embodiment of atop-down fabrication method used to produce an array of dual-disk MRS.In this embodiment, titanium and gold are evaporated onto a wafersubstrate and successive layers of nickel, copper, and nickel areelectroplated or evaporated onto the substrate at step 1. A liftoffresist layer is formed by spincoating, patterning, exposing, anddeveloping photoresist at step 2. A nickel layer is evaporated at step3, and the lift-off photoresist layer is removed at step 4. Copper isevaporated or electroplated at step 5, and steps 2 and 3 are repeated atstep 6. The lift-off photoresist layer is again removed at step 7. Thecopper is wet-etched at step 8. Alternatively, another layer ofpatterned photoresist may be formed, and then the nickel layer may beion-milled prior to the wet etching of the copper in step 8. If desired,external support posts may be formed using similar methods to thosedescribed above.

FIG. 37A-37E is a schematic illustration of an additional embodiment ofa top-down fabrication method used to produce an array of dual-disk MRS.In this embodiment, titanium and gold are evaporated onto a wafersubstrate and circular openings with re-entrant undercut sidewallprofiles are patterned into a double-layer resist stack consisting of anisotropically developing lift-off resist (LOR) beneath a normalphotosensitive resist layer at step 1. To reduce undesired lateraldisplacement and distortion of evaporated structures that result fromnonperpendicular evaporation incidence angles, a thin photoresist layerof no more than 1 μm thickness is used and the LOR layer height reducedto just 1.25 times the desired total height of the evaporated metalstack. At step 2, the base nickel, sacrificial copper, and top nickellayers are evaporated sequentially with all evaporation sourcespositioned directly beneath the wafer center to ensure correctlyoverlaying metal layer alignment. The copper source may be of a largersize than the nickel source to ensure that the deposited copper layersare of slightly greater diameter than the deposited nickel layers toavoid overlap of the nickel layers down the side of the copper layer. Asthe metal deposition proceeds in step 2, metal build-up around thephotoresist sidewalls shrinks the mask hole diameters. The resist maskis removed in step 3, yielding final circular stacks that are not rightcylinders but tapered conical frustums, as shown in FIG. 38. However,the effect of this tapering is corrected for by depositing a thinner topnickel layer than the base layer in step 2 of FIG. 37. A timed copperwet-etch may be used in step 4 to form single copper central postsbetween the upper and lower nickel disks. Alternatively, a shortselective copper wet-etch may be used to expose the edges of the basenickel layer, providing contact area for external spacer posts that arepatterned before the remaining copper is removed, as in step 5. Ascanning electron micrograph of dual-disk MRS resulting from thisfabrication process are shown in FIG. 39.

Various alternative permutations and combinations of the steps of theexemplary top-down fabrication embodiments shown above could equallywell be used to construct dual-disk magnetic resonance structures, solidsingle-disk magnetic resonance contrast agents, and any other magneticresonance structure described above. The particular steps selected maydepend on factors including the absolute structure sizes and aspectratios. Such other manufacturing techniques and structures made therebyare included within the various top-down embodiments.

The materials selected for fabrication of the MRS are not limited to thematerials disclosed in the exemplary top-down fabrication methods, butmay be any magnetic and/or non-magnetic material described previously.Further, the MRS produced using a top-down fabrication method mayfurther incorporate steps to fabricate one or more coatings, includingan oxidation or corrosion barrier, a mechanical strengthening layer, anon-toxic coating, a biologically inert coating such as titanium, or acoating to facilitate common bioconjugation protocols such as gold.

The various embodiments of the MRS are not limited to those produced byonly the top-down methods described above or to these specific top-downmethods of manufacture.

(2) Top-Down Fabrication of Hollow Cylinder MRS

The hollow-cylinder MRS may be fabricated using any one of at leastseveral top-down fabrication techniques. The nanoscale lateraldefinition of the high-aspect-ratio walls of the hollow cylinder MRS maybe challenging to achieve using the traditional top-down fabricationmethods such as the various planar microfabrication methods describedabove. The hollow cylinder MRS may be fabricated using a top-downtechnique that incorporates an unconventional local resputtering of aprepatterned substrate. This local resputtering fabrication methodincludes the novel step of ion-milling away a thin magnetic layerpreviously evaporated onto a substrate patterned with an array of solidcylindrical posts. During the ion-milling, a fraction of the magneticmaterial emitted from the substrate redeposits on the post sidewalls. Bydissolving the post material, cylindrical magnetic nanoshells having ahighly uniform cylinder wall thickness are formed. This uniformity ofcylinder wall thickness over the full length of the cylinder results inwell-defined and sharp NMR spectral peaks, as illustrated in FIG. 19B.

FIG. 20A summarizes the geometry used for the following description ofthe sputter-coated wall thickness as a function of cylinder height z, upthe side of a cylindrical post. The sputtered coating may naively beexpected to be much thicker at the base of the post than at the top ofthe base since points near the base are closer to the source ofsputtered substrate atoms than those regions higher up the post.However, because the sputtered atom distribution is not isotropic withrespect to height above the substrate, the resputtered wall thickness isunexpectedly uniform. According to linear collision cascade theory,sputter distributions are to first order proportional to cos θ, where θis the angle between the direction of sputtering and the normal of thesubstrate surface. Sputter distributions have been shown to possessunder-cosine distributions, cosine-like distributions, and over-cosinedistributions depending on the incident ion energies. The angulardependencies of the sputter distributions may therefore be generallyapproximated as proportional to cos^(m) θ, with values of m below orabove unity representing under- or over-cosine distributions,respectively.

Referring back to FIG. 20A, a normally incident ion beam may removeN_(s) substrate atoms per unit area or an equivalent amount ofN_(s)rdrdφ atoms from a differential substrate element P. At a distanced away from the substrate element P, the substrate element P yields anatom fluence per unit area of n_(s)(d)·cos^(m)θ. The proportionalitycoefficient n_(s)(d)=(m+1) N_(Σ)ρδρ δφ/(2πδ²) may be determined bynormalizing the integrated fluence through a hemispherical surface ofradius d that is centered on substrate element P, using the number ofatoms emitted. Including the projection factor cos ø sin θ to accountfor the angle between the atom fluence and the cylinder surface normal,the number of atoms striking the cylinder per unit area at somerepresentative point Q may then be expressed as z^(m)·(m+1)·N_(s)·cosø·r²drdø/(2π(r²+z²)^((3+m)/2)), where cos θ, sin θ and the distance PQ,are expressed in terms of r and z. Integrating over the half of thesubstrate visible from point Q then gives the total number of atomsN_(c) hitting the cylinder per unit area at height 0<z<L as expressed inEqn. (9):

$\begin{matrix}{{N_{c}(z)} = {N_{s}\frac{z^{m}( {m + 1} )}{\pi}{\int_{0}^{R}{\frac{r^{2}}{( {r^{2} + z^{2}} )^{{({m + 3})}/2}}\ {dr}}}}} & (9)\end{matrix}$

where R is a measure of the effective substrate target size. As Rapproaches infinity, physically approximated by R>>L, for all m>0, N_(c)reduces to N_(s)Γ(m/2)/(2π^(1/2)Γ((m+1)/2)) where Γ denotes the gammafunction. Under these assumptions, N_(c) becomes independent of height,implying a uniformly thick wall coating.

Moreover, due to the sputtering anisotropy, approximately uniformcoatings result from using effective target substrate sizes R that areonly a few times larger than L. For example, a cosine sputterdistribution gives N_(c)(z)=(N_(s)/π)[arctan(R/z)−(R/z+z/R)⁻¹], implyinga cylinder wall that deviates from its average thickness by no more than±10 percent over the entire cylinder length for R/L values that aregreater than about 7. Similarly, for a cos² θ sputter distribution,N_(c)(z)=(N_(s)/π)(1+(z/R)²)^(−3/2), implying similar wall-thicknessuniformity for R/L values that are greater than 3. The sputteringanisotropy therefore may facilitate efficient and parallel processing ofrelatively closely packed arrays of structures on a substrate. However,as R/L decreases below the threshold values discussed above,increasingly peaked sputter distributions and higher ion beam energiesmay be necessary to maintain sufficient uniformity of the cylinder wallthickness.

Because excessively high beam voltages are not required to producehollow cylindrical MRS, externally coated arrays of cylindrical postsmay be used instead of internally coated arrays of cylindrical holes.Although the internal coating of cylindrical holes may be used toproduce ring-like structures, the limited sputter target area of thistechnique implies a low effective R/L value and a resulting substantialwall thickness variation for all but very short cylinders.

FIG. 20B illustrates three examples of wall thickness variations basedon solutions of Eqn. (9) for three different sputter distributions. Eqn.(9) also quantifies the absolute wall thickness. For example,simplifying Eqn. (9) for R>>L, a cosine sputter distribution (m=1) givesN_(C)/N_(S)=1/2. Assuming unit-sticking probability, the shell wallthickness is therefore one-half of the thickness of the original layerion-milled off the substrate. In this manner, the nanometer-level heightcontrol common to planar thin-film layers translates into similarnanometer-level width control of thin, vertically oriented surfaces.

Since the previously described analysis was not necessarily limited to acylinder, other high-aspect-ratio structures may be similarlyfabricated. However, because some alternative magnetic resonancestructure geometries may limit substrate visibility, locally differinglimits to the R-integral and ø-integral, and possible couplings betweenthe integrals may exist. In addition, Eqn. (9) is strictly valid onlyfor thin coatings in which t<<L. For thicker coatings, the possibilityof appreciable time-dependent modification to the surface normal assubstantial sidewall material accumulates, ion erosion of theaccumulated material, and reflection from accumulated material may betaken into consideration. While these secondary effects may beessentially negligible for the high aspect-ratio thin-walled structuresdescribed above, general theory describing these secondary effects areknown in the art.

FIGS. 21A-21F provide a schematic illustration of one embodiment of atop-down fabrication process for the production of the hollowcylindrical MRS. Cylindrical posts of radius p are patterned out of aphotoresist layer of thickness L atop a sacrificial gold layer, as shownin FIG. 21A. To avoid resist exposure to the ion beam, and to facilitatesubsequent structure release, a thin sacrificial copper layer isevaporated obliquely on the substrate and posts, as shown in FIG. 21B,coating the substrate everywhere except within the shadows cast by thecylindrical posts. The desired magnetic material is evaporated as shownin FIG. 21C, and removed from the substrate and the tops of the postsvia argon ion beam milling as shown in FIG. 21D leaving behind theredeposited sidewall coatings as described above. A selective wet-etchof the underlying protective copper followed by an acetone resistremoval then leaves the desired hollow cylinders as shown in FIG. 21E.Each hollow cylinder at this stage is attached to the substrate aroundjust one half of the base, corresponding to the shadowed sides that didnot receive any copper coating previously, holding the hollow cylindersin place on the substrate for further processing, if desired. Thecylindrical shells may be removed from the substrate by either a gentleultrasound treatment or a selective wet-etching of the underlyingsacrificial layer (FIG. 21F). Note that the copper layer is notessential in this method, but including the copper layer facilitates theresist removal and provides the option of a subsequent water-basedultrasound release free of any metal etchants or solvents.

For the case of cylindrical posts the magnetic material evaporation mayalso be performed at an oblique angle in a manner similar to the copperevaporation step shown in FIG. 21B, provided that the substrate iscontinually rotated throughout the evaporation of the magnetic material.However, if oblique evaporation is used to coat the post sidewalls withmagnetic material, this material may also coat the substrate, andtherefore still require subsequent ion-milling, subjecting the cylindersto similar sidewall sputter redeposition. The oblique rotatingevaporation of magnetic material may be conducted at shallow grazingangles relative to the substrate, but then the shadowing resulting fromthe shallow grazing angle may limit the general applicability of thistechnique and the spatial density of structures that may be patternedusing this technique. Although coating the substrate with evaporatedmagnetic material may also be avoided by obliquely shadow-evaporatingonto an inversely patterned array of cylindrical holes rather thanposts, such geometries may preclude uniformly thick wall coatings.Because of the circular cylinder cross-sections, the line-of-sightpenetration depths of evaporant material may vary across each hole,resulting in cylindrical shells whose wall thicknesses taper down fromtop to bottom.

FIG. 22A is a scanning electron micrograph (SEM) of a sample array offabricated nickel hollow cylindrical MRS that have undergone a partialwet-etch release. The cylinders have wall thicknesses of about 75 nm,cylinder inner radii of about 1 μm, and an aspect ratio (L/2ρ) of about1.2, implying wall height-to-thickness aspect ratios L/t of about 30.Despite having thin walls, the hollow cylindrical structures arephysically robust, self-supporting structures that are resistant todamage during either wet-etch (see FIG. 22A) or ultrasound release (seeFIG. 22B). In FIG. 22B, the hollow cylindrical structures were removedfrom the substrate using ultrasound, transferred into a vial of water,and then pipetted out onto fresh substrates. When the fresh substrateswere placed into an applied background magnetic field, the hollowcylindrical MRS aligned with the applied field direction due to theanisotropy of the hollow cylinder's structure imparted by the high L/taspect ratios of the structures, as shown in FIG. 22B.

These fabrications of hollow cylinder MRS are not limited by size,scale, dimensions, materials and/or various layers that may be used ascoatings and adhesion layers.

(3) Top-Down Fabrication of Solid Particulate MRS-Single Disc

The solid particulate MRS agent may be microfabricated through thetop-down method. The top-down fabrication can include the micromachiningmethods of using metal evaporation, ion-milling and lift-offmicropatterning techniques. Photolithographic patterning may be used togenerate arrays of many of millions of solid particulate MRS to besimultaneously fabricated. A substrate may be used to generate the solidparticulate MRS.

An exemplary process of generating solid particulate MRS is shown inFIG. 41. A 10-nm thick titanium adhesion layer may be evaporated onto asupporting substrate followed by a 100-nm thick sacrificial copper layerand a 100-nm thick gold layer at step 1. Also at step 1, a double layerof resist may be spin-coated over the titanium-copper-gold trilayer witha photosensitive top layer of resist and a bottom layer of isotropicallydeveloping lift-off resist. This structure may be exposed through a maskcontaining an array of 2 m-diameter circular holes at step 1 as well.The patterned development and dissolution of the top resist layerresults in the isotropic development and dissolution of those physicallyexposed portions of the lift-off resist, creating the profile shown instep 1. An approximately 300-nm thick layer of iron and/or nickel maythen be evaporated followed by an evaporation of a 200-nm thick layer ofgold at step 2. The metal deposited on the top of the photoresist isphysically disconnected from metal deposited on the substrate in thisstep, and subsequent removal of the resist bi-layer at step 3 may removethe top metal layers while leaving the metal bilayer on the substrateuntouched. A 100-nm deep argon ion-milling may then remove the exposedgold on the substrate and about half of the top 200-nm gold layer atstep 3. During this ion-milling process some of the back-sputtered goldion-milled from the substrate may redeposit on the iron/nickelsidewalls, leaving magnetic disks of nickel and/or iron completelyencased in gold at step 4. The gold encasing the nickel and/or iron maybe in the form of a 100-nm thick top and bottom gold coatings, andapproximately 50-nm thick gold coatings around the circumferentialsidewalls of the disks. Finally a selective wet-etch of the underlyingcopper or treatment with ultrasound may be used to release the particlesfrom the substrate (not shown). The particles may also be washed toremove any remaining etchant solution.

These fabrications of solid particular MRS are not limited by size,scale, dimensions, materials and various layers may be used as coatingsand adhesion layers.

b. Bottom-Up Fabrication

The bottom-up method may be a chemical synthesis technique, which maynot include at least one spatial patterning step. The bottom-up methodmay use tightly-controlled process specifications, or an additionalsorting step to select a sub-group of MRS having acceptably similargeometric and compositional properties.

Where only a few distinct spectral shifts induced by the MRS are to beused in magnetic resonance visualization at any one time, it may bepossible to sacrifice some fabrication precision in order to make use ofbottom-up fabrication techniques. Certain well-controlled chemicalsyntheses may possess a high enough degree of control and monodispersityto provide practical fabrication methods for the MRS.

A large batch of the MRS may be synthesized and then separated and/orfiltered step to select out only those structures from the large batchthat have geometrical shapes that fall within a suitably narrow band ofsizes and shapes. The typically higher throughput of chemical synthesismethods may render this approach suitable for some applications.

A filtering/separation step may be accomplished by taking advantage ofthe magnetic moment and magnetic materials of the MRS. For example, witha batch of structures fabricated using a bottom-up method suspended insome fluid, an external magnet field gradient may be applied to create aforce on the structures that drags them through the fluid. In thisexample, the speed of the particles moving through the fluid may begoverned by a balance between the drag force of the fluid on theparticles and the translational magnetic force acting on the particles.However, the magnetic and drag forces may depend on the shapes andmagnetic moments of the particles to differing degrees. Therefore, aftermoving through the fluid under the influence of the applied magneticfield gradient, the differently sized/shaped/composed particles may bespatially separated within the fluid, and a sub-group of the particlesmay be specifically selected from the fluid based upon their locationwithin the fluid. The particles within this particular sub-group mayexhibit a suitably high degree of monodispersity and may have thedesired shapes.

The MRS may be formed using a template structure such as a porousmembrane substrate formed from a porous material known in the art suchas anodic alumina. The cylindrical pores within the template structuremay be filled with one material, the template structure may bechemically treated to enlarge the pore sizes, forming annular ringsbetween the cylinders and the eroded template structure within eachfilled pore. The annular ring may then be filled with a magneticmaterial and the inner material may be chemically eroded to form hollowcylindrical structures that may be removed by again eroding the templatestructure by selective chemical removal.

To fabricate the MRS, an ensemble of solid cylindrical rods suspended ina solution may be chemically coated with a magnetic material using achemical method such as electroless plating, or galvanic deposition. Forexample, commercially available gold nanorods may be suspended in anelectrolyte solution. However, prior to chemically coating thecylinders, the ends of the cylinders may be selectively chemicallypassivated to ensure that the plating of the magnetic material occurredonly around the sides of the cylinders. The central cylinders may thenbe selectively etched out, leaving only the plated cylindrical shell.Because typical existing cylindrical rods exhibit considerable variationin diameter and length, an optional filtering/separation step may beperformed as previously described to select a sub-group of hollowcylinders having the desired shape and composition.

4. Methods of Use

The MRS may be used in a variety of applications, in addition toproviding magnetic resonance frequency-shifting contrast. On a smallscale, the MRS may be used to mark various objects as a microtag or as acell marker. The alignment of anisotropic MRS to an applied magneticfield may be used to determine the direction or other characteristics ofa flow. On a large scale, the MRS may be installed around the perimeterof a variety of fluid-carrying vessels ranging such as microfluidicschannels or blood vessels and used to frequency-shift the fluid passingthrough the reserved space of the MRS, providing spin-tagged flow formagnetic resonance flow visualization.

Shifts in the Larmor frequency of water protons or other NMR-susceptiblenuclei within a near-field region of the MRS during exposure to aresonant electromagnetic pulse may be used to conduct multiplexed colormagnetic resonance visualization. Engineered to exploit diffusion and/orfluid flow in some embodiments, the MRS increases existing magneticresonance sensitivity by orders of magnitude, and reduces the requiredconcentrations of the MRS to well below those of existing contrastagents. The MRS may additionally function as an individually detectable,spectrally distinct micro-tag. With NMR spectral shifts determined bystructural shape and composition instead of by chemical or nuclearshifts, the spectral signatures associated with the MRS may bearbitrarily tailored over uniquely broad shift ranges spanning many tensof thousands of parts per million. The MRS having a size scale ofmicrometers may function as a localized physiological probe, enhancingboth magnetic resonance capabilities and basic biological research. TheMRS may also be used over a wide range of applications that areanalogous to the uses of quantum dots or RFID tags.

a. Dephasing Contrast Enhancement Agents

(1) Solid Particulate MRS Contrast Agents

The solid particulate MRS may be used as conventional T₂* contrast agentdue to its magnetic materials. The solid particular MRS may be spatiallyimaged using the same dephasing contrast analysis common to MPIOs.Because the top-down manufacturing technique is amenable to the use ofhigh J_(s) materials such as iron, the solid particulate MRS contrastagents possess higher magnetic moments for a given particle volumecompared to existing contrast agents such as MPIOs. As a result, solidparticulate MRS contrast agents may be used to achieve comparablecontrast levels at lower concentrations than existing contrast agentssuch as MPIOs.

(2) MRS with Reserved Space as Dephasing Contrast Agent

In addition to acting as a conventional T₂* contrast agent, an MRS witha reserved space may be differentiated spectrally using the additionalinformation provided by the NMR-shifting capabilities of the reservedspace. For example, the NMR-shift information may be used to distinguishcontrast signals from spurious signal voids that confound magneticresonance imaging using SPIO or MPIO contrast agents. Depending on thesize of the MRS, multiple different particle spectra may be acquiredsimultaneously from a single free induction decay signal following ahard π/2 excitation pulse. Alternatively, magnetic resonance imaging mayspectrally resolve the tags separately, as shown for example in FIG. 11.

b. MRS Identity System

The MRS may be used as a microtag to mark a variety of items with aunique color frequency-shift. This frequency-shift may be measured usinga MRS identity system. An MRS microtag may be used to mark virtually anyitem to which one or more MRS may be attached, or a container containingone or more MRS microtags that may be attached. For example, MRSmicrotags may be used to mark biological cells for cell trackingstudies, packages for tracking during shipping, and inventory forindustrial inventory control.

FIG. 5 is a system diagram of an embodiment of a magnetic resonanceidentity system 200. The magnetic resonance identity system 200 includesat least one MRS 202, a source of electromagnetic radiation 204 toilluminate the magnetic resonance microstructure 202 with an excitatoryelectromagnetic pulse, and a detection system 206 to detectelectromagnetic radiation emitted from within the magnetic resonancemicrostructure 202 after the MRS 202 has been illuminated with the anexcitatory electromagnetic pulse. The MRS 202 may be a solid particulateMRS that functions solely as a T₂* contrast agent, or an MRS with areserved space that may act as either a T₂* contrast agent, aNMR-shifting contrast agent, or both. The magnetic resonance identitysystem 200 may also include a magnetic field generation system 208 toprovide a magnetic field in a region suitable for the placement of asample of interest that may include the MRS microtag.

c. MRS Stent

A stent that includes an MRS with a reserved space may be used tomonitor blood flow through the stent as well as remotely monitoring thecondition of the stent. Discrete volumes of NMR-shifted water protonscreated at different times within the reserved space may be visualizedusing NMR imaging and used to estimate the blood flow speed downstreamof the stent. In addition, the magnitude of the NMR-shift may measuredand used to determine changes in the condition if the stent collapse ortheir is distortion of the stent.

The MRS may be installed around the inner or outer perimeter of a stentin order to measure the characteristics of blood flow through the stent.Alternatively, the stent may be entirely composed of the MRS structure.The stent is situated such that the blood flow passes through thereserved space of the MRS.

FIG. 25 is a schematic illustration of an embodiment of a hollowcylindrical MRS that functions in conjunction with a stent. In thisembodiment, a thin ring-like magnetizable solid structure surrounds oris attached to the inside walls of a stent device. The MRS of thisembodiment may also be one or more dual-disk MRS, as shown in FIG. 26.If more than one dual-disk MRS are used, each pair of disks may besituated at the same longitudinal position along the stent, but rotatedaround the stent's axis of symmetry by different rotations angles. Theremay also be a plurality of dual-disk MRS arrayed around at differentangles to approximate a ring structure.

The particular magnetic resonance structure may be selected based on thetype of stent in which the structure is to be used. For example, adual-disk geometry may be more favorable geometry if the stent device isintended to be inserted in a collapsed position and then expanded via acatheter balloon after the stent is situated in its intended location.

The spectral shifting within the reserved space of the MRS allows thewater protons or other NMR-susceptible nuclei in the blood flowingthrough the MRS to be spin-labeled so that blood flow (both speed and,through frequency-shift-dependent stent diameter indications, mass-flow)can be measured. Such spin-labeling, alternatively also known asspin-tagging, can be performed by, for example, irradiating the MRS withresonant RF electromagnetic pulse to specifically spin-tagNMR-susceptible nuclei within the reserved space. Fluid not residentwithin the reserved space during a resonant RF electromagnetic pulsewould be essentially unaffected by the pulse.

Should the artery or other blood vessel containing a stent narrow, thestent diameter may shrink as a result, causing the NMR frequency shiftto be altered, as discussed above and shown in Eqn. (2) and/or Eqn. (7),due to the change in spacing between magnetizable elements. A similareffect may occur if the stent itself was in some way damaged or startedto collapse. Thus, the inclusion of MRS within a stent device enablesthe non-invasive NMR measurement of artery collapse or warning ofpossible imminent stent collapse.

There may also be multiple NMR spaced at pre-determined intervalslongitudinally along the stent in some embodiments of the currentinvention to provide redundancy, to be used for alternative blood flowspeed measuring (for example via time-of-flight techniques), or toincrease the contrast signal magnitude. A similar measurement of bloodflow within a blood vessel may be non-invasively measured without astent device by placing the magnetic elements of the MRS arrayed aroundthe outside of a vein/artery or other blood vessel to monitor blood flowwithin that blood vessel.

d. Spin-Tagging Fluid Flow/Perfusion Imaging

MRS may be situated such that a fluid flows through the reserved space,and a volume of fluid within the reserved space may be frequency-shiftedby the uniform magnetic field of the MRS. For a limited period of timeafter leaving the reserved space, the volume of fluid may retain theshifted NMR frequency, effectively spin-tagging the fluid as it flows.Using magnetic resonance visualization methods described above, thespin-tagged fluid may be visualized and analyzed to determine a varietyof flow characteristics such as flow speed.

To perform the spin-tagging of fluid flow, one or more MRS may besituated around the perimeter of a fluid vessel and/or along the lengthof a fluid vessel and the fluid flowing through the reserved space ofthe MRS may be frequency-shifted and visualized using magnetic resonancetechniques to provide non-invasive visualization of fluid flow. Thisconcept of spin-tagging fluid as it passes through the uniform magneticfield within the reserved space of the MRS structures may be used at avariety of size scales ranging from vessels that are about 1-μm, 2-μm,5-μm, 10-μm, 20-μm, 30-μm, 40-μm, 50-μm, 60-μm, 70-μm, 80-μm, 90-μm,100-μm, 200-μm, 300-μm, 400-μm, 500-μm, 600-μm, 700-μm, 800-μm, 900-μm,1 mm, 2 mm, 3 mm, 4 mm, 5 mm diameter to vessels that are about 5 cm ormore in diameter. Fluid flows that may be visualized using MRSspin-tagging methods may include perfusion and other blood flow,industrial fluid flow, and flow in microfluidic systems. For example,applications may include measuring, imaging, or detecting flow within amicrofluidic channel or network as may exist in various microchip-basedchemical and biological assays (i.e., lab-on-a-chip systems). As anotherexample, the flow in industrial pipes or pipelines may be visualizedusing spin-tagging of the fluid within the pipes using one or more MRSthat may be arrayed externally about the exterior circumference of thepipes, or contained within the pipes or attached to the inner walls ofthe pipes. Spin-tagging using MRS may further provide flow monitoringcapabilities even if the pipes are non-transparent. Flow monitoringcapabilities may include observing where fluid subsequently flows,measuring the flow speed, and how the flow speed varies across one ormore cross-sections of the pipe or along the length of the pipe.

The MRS may be used to spin-tag discrete volumes of fluid containingNMR-susceptible nuclei such as water protons by exposing the MRS todiscretely spaced electromagnetic pulses at the resonance frequency ofthe MRS. Fluid contained within the reserved volume during each resonantelectromagnetic pulse is phase-shifted, and any remaining fluid outsideof the reserved volume is unaffected by the resonant electromagneticpulse. Fluid flowing downstream of the MRS that has been phase-shiftedin this may be visualized using magnetic resonance visualization. FIGS.28 and 29 are MRI images showing the bands of spin-tagged fluiddownstream of an MRS. In FIG. 28, both pipes in the figure were exposedto a discrete series of electromagnetic pulses at the resonant frequencyof the left MRS prior to MRI scanning. In FIG. 29, both pipes wereexposed to a discrete series of electromagnetic pulses at the resonantfrequency of the right MRS prior to MRI scanning. Each dark band in thepipes mark the parabolic profile of a spin-tagged volume that hastraveled in a laminar flow within the pipe for a short distancedownstream from the reserved volume. In addition, because the right handpipe in FIG. 28 was not exposed to an electromagnetic pulse at itsresonant frequency, which is different from the resonant frequency ofthe left MRS, none of the flow in the right pipe was spin-tagged,resulting in a uniformly light image in the MRI image. The flow in theleft pipe in FIG. 29 was not spin-tagged for similar reasons.

Additionally, the MRS may be used to conduct perfusion studies withmultiple spin-labeled streams that are immune to magnetic mixing. Such aprocess may also be applied to perfusion imaging where the resonantelectromagnetic labeling pulses are spaced close enough in time so as toappear continuous in an image, as shown in FIGS. 30 and 31 for the leftand right tubes, respectively, where in this case the spin-labeled flowoccupying half of each tube is darkened. For example, this technique maybe used to show where fresh blood enters the brain and perfuses.

The spin-tagging technique of flow visualization may be used to measurethe features of both laminar Poiseuille flow, as well as turbulent flow.Finer flow features such as turbulence, vortex structure, or boundarylayer structure may be measured using spin-tagging, so long as themagnetic resonance visualization device used to visualize thespin-tagged flow possessed sufficient resolution.

e. Magnetic Resonance Spatial Calibration Markers/Locators (when Affixedto Substrate)

An array of MRS with known separation distances and angles may be usedas a calibration aid for a magnetic resonance device. A set of the MRSmight be arrayed in some regular geometrically prescribed arrangementwith known spacings and/or angles between the individual MRS in the set,firmly attached to a rigid substrate to provide a spatial calibration ofmeasured distances and angles in a magnetic resonance device. If MRSwith reserved spaces are used, MRS with two or more frequency-shiftingcharacteristics may be placed in close proximity within the set, evenwithin the same voxel of the magnetic resonance device, so long as theMRS are separated by at least about twice the maximum dimension of theMRS. Using multi-spectral scanning methods, in which the calibration aidis imaged after each exposure to electromagnetic pulses at each of theresonant frequencies of each subset of the MRS in the calibration aid. Amuch higher calibration resolution may be achieved than is possibleusing MRS with uniform contrast properties or existing magnetic particlecontrast agents.

In addition, the MRS may be attached to a moving substrate within thefield of view of an MRS device. For example, an MRS may be attached tothe tip of a surgical instrument such as a catheter, and magneticresonance visualization may be used to track the location of thesurgical instrument non-invasively and/or guide the surgical instrumentduring a surgical procedure.

If an MRS with a reserved space is attached to a surgical instrument orother moving substrate, the NMR-shifting signal of the MRS may be usedto identify the particular moving substrate as it moves within the fieldof view of the magnetic resonance device. Each of two or more surgicalinstruments may be marked with MRS with different NMR-shifting signalfrequencies and the movements of each surgical instrument may beindividually tracked and guided using the multispectral magneticresonance visualization methods described above. Further, cells ortissues to be targeted by the surgical instruments may be marked withyet another group of MRS having another NMR-shift signal frequency toprovide a target for the surgical instruments using multispectralmagnetic resonance visualization.

An activatable MRS, described above, may be attached to a movingsubstrate such as a surgical instrument and used as a smart sensor inwhich the NMR frequency shift changes as a function of somephysiological condition such as temperature, oxygen content, or pH. Forexample, as the moving substrate is moved within the field of view ofthe NMR visualization device, such as during a surgical procedure, theNMR frequency shift of the MRS may be monitored to assess one or morephysiological conditions in order to monitor the conditions of asurgical procedure or to guide the placement of the surgical instrument.

f. MRS Microtags and Specific Detection/Labeling/Tracking of BiologicalCells

One or more MRS microtags may be affixed to an object, allowing thatobject to be magnetically probed and/or recognized using the magneticresonance visualization techniques described above. Unique combinationsof MRS about 1-μm to about 1-mm in overall size may be used to label anobject such as a cell, organism, or non-biological object foridentification using magnetic resonance scanning. The identificationinformation may be encoded by the combinations of MRS in a manneranalogous to RFID-tagging. In addition, by marking each object with oneor more different MRS particles having different frequency shifts,different objects may be distinguished from each other in much the sameway as regular RFID chips do by marking the object with one or more MRShaving a specific known NMR frequency shift, except that the identifyingsignal is based on a nuclear magnetic resonance measurement. Forexample, objects of type A may be marked with a MRS having a NMRfrequency shift A, and another object B may be marked with a differentMRS having a NMR frequency shift B.

The MRS particles and the objects that they label may reside within afluid, gas, or gel suitable for magnetic resonance probing, or the MRSparticles may be packaged in a separate container along with some amountof fluid, gas, or gel, and the entire container and MRS particlescontained within may be affixed to the object as a marker. TheMRS-tagged object need not itself be within the fluid or gel in order tobe marked.

One or more MRS may be bound to or incorporated within certainbiological cells to mark the cells for subsequent magnetic resonancevisualization studies. In this example, the MRS might include a specificbiochemical coating ensuring that the MRS specifically binds to aspecific cell type. This would enable tracking of cells and inparticular, the ability to differentiate between different cell types byexploiting the different frequency shifts of the attached MRS.

A biological cell labeled with several solid-disk MRS attached to theouter cell membrane is shown in FIG. 52. A biological cell labeled withseveral solid-disk MRS that have been incorporated into the cytoplasm ofthe cell is shown in FIG. 53.

The objects marked using MRS microtags may be in placed in stationarycontainers, or the objects may be situated within a vessel containing amoving flow of a fluid. For example, MRS microtags may be used to labelobjects flowing in a microfluidic steam, so that remote sensing andidentification of the labeled objects may be made as they aretransported within the microfluidic steam. Because this method makes useof magnetic resonance visualization techniques, an optical line of sightis not required to identify the objects, unlike existing microfluidicsidentification methods. As a result, this method may also be useful formonitoring microfluid flows in otherwise inaccessible locations within amicrofluidics device.

In another example, living biological cells may be labeled using one ormore MRS microtags functionalized with specific antigens or otherbinding agents in order to label particular flow types. In this example,flow cytometry may be conducted by inducing the cells to flow past amagnetic resonance sensor. Alternatively, living cells such as bloodcells may be labeled as they circulate using one or more MRS microtags,and in vivo flow cytometry may be performed by sensing the labeled cellsusing a magnetic resonance scanner focused in a specific region of ablood vessel of a living subject. In yet another example, individuallabeled cells may be tracked as they move within the circulatory vesselsor other tissues or organs of a living subject.

The overall size of the MRS used to label living cells ranges from about1 μm to about 10 μm, or may be about 1 μm, 2 μm, 3 μm, 4 μm, 5 μm, 6 μm,7 μm, 8 μm, 9 μm, or 10 μm. The minimum overall size is limited to thesmallest particle that is still visible using nuclear magneticvisualization, and the maximum overall size is limited to the largestparticle that may be placed in the cytoplasm of a living cell withoutadversely affecting the viability of the labeled cell. In addition, inorder to be detectable by a magnetic resonance device, the MRS microtagmust have a magnetic moment of at least about 10⁻¹³ Am². The MRSmicrotags may be affixed to the outer cell membrane or cell wall, or theMRS microtags may be inserted into the cytoplasm of the labeled cell.The MRS microtags may be introduced into the cell by endocytosis meanssuch as phagocytosis, macropinocytosis, caveolae, clathrin-mediatedendocytosis or receptor-mediated endocytosis. MRS microtags may also beintroduced by genetic engineering methods such as electroporation orprotoplasts.

Apart from identifying or tracking labeled objects moving in stream,this method may also be used to infer additional information about thefluid stream, such as flow speed by noting how the MRS microtags movewithin the stream.

g. Magnetic Field Sensors

An array of MRS particles in which each MRS particle has a slightlydifferent frequency-shifting behavior may be placed within a magneticfield in order to measure its strength. Because the resonance frequencyof the MRS determines an offset in the Larmor precession frequency ofthe nuclear magnetic moments that pass through the reserved space of theMRS, the exact absolute resonant Larmor precession frequency induced bythe MRS may be used to provide a visual measure of the total magneticfield created by the superposition of the magnetic field within thereserved space and the external magnetic field. Because the magnitude ofthe magnetic field within the reserved space may be determined from thegeometry and materials included in the MRS, the magnitude of theexternal applied magnetic field may be determined by subtracting theknown magnetic field from the reserved space from the total magneticfield deduced from the frequency shift induced by the total magneticfield.

Alternatively, a uniform geometrical array of MRS particles may bearranged with the geometry of each MRS particle varied such that eachfrequency shift differs by a predetermined amount from the frequencyshift of the neighboring MRS particles. Within the array, neighboringMRS may be spaced at least about 2-3 times the maximum outer dimensionof the MRS away from all neighboring MRS to minimize the interaction ofneighboring MRS external magnetic fields.

A magnetic resonance image of this array would show higher or lowersignal amplitudes at a specific location in the array due to thefrequency-shifting effects of the external magnetic field. Using thisMRS particle array, the measurement of the magnetic field is effectivelytransformed from a field measurement method into a method of visuallylocating the spatial position of the higher or lower signal, anddetermining the field strength from the known frequency-shiftingcharacteristics of the MRS particle at that location.

h. Distance/Pressure/Vibration/Torque Sensors (all Will Affect theParticles Measurable Frequency Shifts Through Change in ParticleGeometry)

The MRS may be designed so that the frequency-shifting behavior maydepend on a physical factor such as pressure, vibration, orientationchanges, or torque experienced by the MRS. Magnetic resonancevisualization of an MRS with this design may be used to non-invasivelyassess physical forces within a living subject or within anotherstructure or fluid flow. Because the frequency-shifting of the MRSdepends on, among other factors, the spacing between the magneticportions and the orientation of the MRS relative to the backgroundmagnetic field, an MRS may be used to measure a variety of physicalphenomena by transducing these phenomena into a distance change betweenthe magnetic portions.

For example, an MRS may be designed to have a diminished ability toself-align to an applied magnetic field direction. Because thefrequency-shifting behavior of the MRS also depends on its alignmentwith an applied magnetic field, changes in the frequency-shifting signalfrom an MRS with this design may be used to assess the degree ofalignment with the external magnetic field. By altering theself-aligning behavior relative to the tendency to align with otherapplied forces such as fluid dynamic torques, the strength of thefrequency-shifting signal may be used to measure the magnitude of theother applied forces.

Such orientation sensing may also be used to map fluid flow direction orfor measuring fluid flow strength. For example, if the fluid dynamicforces were stronger than the magnetic self-alignment forces, then theorientation of the MRS, as measured by the strength or existence of thecharacteristic spectral signature of the MRS, may depend on the fluidflow direction relative to the direction of the applied magnetic field.Vasculature network geometries that may be too small to be visualizedusing existing magnetic resonance techniques may be mapped using themagnetic resonance visualization of an MRS with this design. Inaddition, fluid flow strength may be measured by observing whether ornot the applied magnetic field is suitably strong to realign an MRSsituated within a fluid flow.

Different portions of the magnetic material within an MRS may bedesigned to change orientation with respect to each other in reaction toan applied force or torque. The change in the relative orientation ofthe different portions of the magnetic materials alters thefrequency-shifting of the MRS with this design. The changes infrequency-shifting behavior of the MRS, as measured using magneticresonance visualization methods, may be used to provide an indirectmeasure of one or more torque forces acting on the MRS, or simply adifferent angular orientation of the MRS.

For example, if a double-disk MRS with one disk fixed to a rigid surfaceis placed into flow of sufficient velocity, the shear forces of themoving fluid acting on the unattached disk may exert a force thatdisplaces the free disk relative to the immobilized disk, causing theNMR frequency-shift signal to cease. The system may be calibrated suchthe MRS stops producing a NMR frequency-shift signal at a known flowspeed or shear force, or any array of MRS in which each MRS having adifferent NMR frequency-shift stops producing NMR frequency-shiftsignals at a different predetermined flow speed or shear force.

In another example, an MRS may be designed to measure fluid pressures inthe blood stream. In this example, the alignment of the MRS with respectto the magnetic resonance magnetic field may be governed by anequilibrium between the magnetic self-alignment torques of the MRS fromthe magnetic resonance magnetic field and the rotational and/or shearforces exerted by the flowing fluid.

In yet another example, two or more MRS having differentfrequency-shifting characteristics may be attached to differentlocations along an object such as a protein molecule. The distancebetween the two different MRS may be estimated using the NMRmulti-spectral imaging data. If the two MRS move to within 2-3 times theMRS size of each other, the NMR-shifting signals cancel each other outdue to the mutual interference of the external magnetic fields of thetwo MRS. Thus, very small distances may be detected using the disablingof the MRS signal, in a manner analogous to fluorescence resonanceenergy transfer (FRET) measurement techniques.

In another example, a fluctuation in the frequency-shift magnitude maybe used to sense vibrations using any of the MRS configurationsdescribed above.

i. Magnetic Separation

Being magnetic, these microstructures could be used in the same manneras regular magnetic beads in traditional magnetic separation protocols.

j. As Rotators of Objects Attached to them/Magnetically Driven RotaryPump-Like Motion/Fluid Pump/Mixer

The MRS particles may be rotated indirectly using a rotating externallyapplied magnetic field and used to act as micropumps or micromixers in avariety of systems. A MRS particle may be designed with a high degree ofmagnetic shape anisotropy, resulting in a relatively high self-aligningmagnetic torque between the MRS particle and an external appliedmagnetic field. By applying a rotating magnetic field to a MRS particlewith a high magnetic anisotropy, a strongly rotating MRS particleresults. This rotating behavior could be exploited to make fluidmicropumps and micromixers.

Such rotation may also be useful for destroying selected biologicalcells such as cancerous cells by placing these microstructures withinsuch cells and then rotating the external field to effectively churn upthe cell's contents. The MRS may be introduced into the cell byendocytosis means such as phagocytosis, macropinocytosis, caveolae,clathrin-mediated endocytosis or receptor-mediated endocytosis. The MRSmay also be introduced by genetic engineering methods such aselectroporation or protoplasts. If the MRS in this example were coatedwith binding agents that specifically bind only to cancerous cells,normal cells would effectively be unharmed using this method. The MRS inthis example may be attached to the outer surface of the cell membraneor cell wall, the inner surface of the cell membrane, or may be insertedinto the cytoplasm of the cell to be destroyed.

The strength of the rotating magnetic field used to rotate the MRS mayrange from about 1 Gauss to 1 Tesla, depending on the size and magneticmoment of the MRS used. The overall size of the MRS used to destroyselected cells using this method may ranges from about 1 μm to about 10μm, or may be about 1 μm, 2 μm, 3 μm, 4 μm, 5 μm, 6 μm, 7 μm, 8 μm, 9μm, or 10 μm Localized RF magnetic heating elements/targeted thermalablation

Depending on the exact material composition of the magnetic portionscomprising these microstructures, application of an alternating magneticfield that repeatedly magnetizes and demagnetizes the objects could beused to generate local heating for targeted thermal ablation/destructionof biological cells such as cancerous cells.

Any non-spherical shape of MRS may be used to destroy selected cellsusing this method, including disks, rods, and cylinders. Any shape ofMRS that includes a sharp edge may be particularly effective indestroying selected cells.

k. Localized Magnetic Field Gradients

The MRS particles may be used in alternative magnetic imaging techniquesthat take advantage of the relatively high localized magnetic fieldgradients external to each MRS. The external magnetic fields of the MRSparticles produced using high Js materials such as iron may induceexceptionally high magnetic field gradients that may be useful foralternate magnetic imaging techniques, or for generating highlylocalized high magnetic forces.

EXAMPLES Example 1 Assessment of Saturation of Dual-Disk MagneticResonance Structures

To assess the effect of the magnitude of applied magnetic field on themagnitude of the induced magnetic field in the reserved volume of amagnetic resonance structure, the following experiment was conducted. A13 mm×13 mm grid of immobilized dual-disk magnetic resonance structureswas tested using an alternating gradient magnetometer to assess themagnitude of the magnetic field induced within the reserved volumes as afunction of the magnitude of the applied magnetic field, as well as thehysteresis of the induced magnetic field during a full alternatinggradient cycle. Each dual-disk magnetic resonance structure in the 13mm×13 mm grid was formed on a 15 mm×15 mm diced Pyrex substrate usingmicrofabrication techniques. Each disk in a dual-disk magnetic resonancestructure was a pure nickel disks having a disk radius of about 2.5 μm,a thickness of about 50 nm, and a disk separation distance of about 2μm. The nickel material from which the disks were constructed had asaturation magnetic polarization (J_(s)) between about 0.5 and about 0.6Tesla. Inter-particle spacings (center-to-center) were typically 3 to 4times the particle diameter to minimize the influence from the inducedfar-field magnetic fields of neighboring particles on the inducedmagnetic field of each individual magnetic resonance structure in thegrid.

A magnetic field was applied to the grid of magnetic resonancestructures that alternated between a value of ±2000×10³/4π A/m, and themagnetic polarization of the dual-disk magnetic resonance structures wasassessed.

The results of the alternating gradient magnetometer measurements aresummarized in FIG. 7. The dual-disk magnetic resonance structuresachieved a saturated magnetic polarization at an applied magnetic fieldof about ±1000×10³/4π A/m, well below the magnitude of applied magneticfield generated by typical magnetic resonance scanning devices.

The results of this experiment confirmed that the dual-disk magneticresonance structures achieved a saturated magnetic polarization atapplied magnetic field magnitudes that are well within the capabilitiesof existing magnetic resonance scanning devices. As such, the fieldshift are independent of the MRI fields.

Example 2 Multi-Spectral Imaging Using Dual-Disk Magnetic ResonanceStructures

To assess the effectiveness of multispectral imaging using magneticresonance structures in a magnetic resonance scanning device, thefollowing experiment was conducted. A grid of immobilized nickeldual-disk magnetic resonance structures were fabricated in a mannersimilar to those described in Example 1. The disks in each dual-diskmagnetic resonance structure in this experiment had a diameter of about1.25 mm and a separation of about 500 mm between the disks.Inter-particle spacings (center-to-center) were typically 3 to 4 timesthe particle diameter to minimize the influence from the inducedfar-field magnetic fields of neighboring particles on the chemicalshifting of each individual magnetic resonance structure in the grid.Subgroups of the dual-disk magnetic resonance structures had diskthicknesses of 4, 6, and 8 μm respectively in order to vary thefrequency shift induced by each respective subgroup. Each subgroup wasarranged on the grid to form the letters R, G, or B, as illustrated inFIG. 11A. Accidental impurities in the nickel discs of these structuresled to a reduction in the saturation magnetic polarization (J_(s)) ofthe disks to about 0.4 T. The disks in each dual-disk magnetic resonancestructure in this experiment were submerged in water.

Free induction decay (fid) signals following a spin-echo were acquiredsweeping through a range of frequencies covering the expected offsetsproduced by the particles. Shaped pulses with a Gaussian profile wereused to limit bandwidth spread into the bulk water peak (as compared toa hard pulse). The bandwidths were sufficient to cover the frequencyprofiles produced by the particles. Acquisitions for the spectra were8192 points in length, covering a bandwidth of −100 kHz. For theassociated RGB image, three 2D chemical shift images were acquired,covering the frequency ranges of the particle spectra. Images areintegrations of the spectra over the different frequency ranges.In-plane resolution was 500×750 μm.

AN image of the grid obtained using gradient-echo (GRE) MRI is shown inFIG. 11B. Magnetic dephasing due to the effects of the far-fieldmagnetic fields induced by the particles enables the spatial imagingshown in FIG. 11B.

FIG. 11C-11E show the chemical shift imaging (CSI) of the gridmagnetized by an applied magnetic field B₀. The additional spectralinformation provided by CSI imaging differentiates between individualparticle types and improves particle localization. The particle spectraof each particle subgroup, as shown in FIGS. 11G-11J were shifted wellaway from the unshifted water proton line. Further, as shown in FIG.11J, the particle spectra are each sufficiently separated, allowing forthe unambiguous color-coding of the individual particle types withminimal background interference.

The results of this experiment demonstrated the feasibility of using thedual-disk magnetic resonance structures to achieve multispectralmagnetic resonance imaging using a chemical shift imaging (CSI) process.

Example 3 Frequency-Shifting of Deuterium Proton Signals by Dual-DiskMagnetic Resonance Structures

To determine the effectiveness of the frequency-shifting of protonsother than water protons, the following experiment was conducted. A gridof dual-disk magnetic resonance structures similar to those described inExample 1 were submerged in deuterium oxide (D₂O) and imaged in a mannersimilar that described in Example 2. In this experiment, the disks inthe dual-disk magnetic resonant structures had a diameter of about 25μm, a disk thickness of about 0.5 m, and a separation distance of about10 μm between the disks. A grid of dual-disk magnetic resonancestructures was constructed similar to those described in Example 1.

An individual pyrex chip was placed in a custom-made holder and filledwith a layer of deuterium oxide (D₂O) to a thickness of about 150 μm, inorder to submerge the particles and provide an additional layer ofdeuterium oxide (D₂O) well above the extent of any appreciable externalmagnetic fields induced by the magnetic resonance structures. Thedeuterium oxide (D₂O)-submerged pyrex chip sample was then placed nextto or inside of the surface or solenoidal coils of the magneticresonance scanning device for transmission/reception of the NMR signal.

Free induction decay (fid) signals following a spin-echo pattern wereacquired in a manner similar to that described in Experiment 2. Thebandwidth of the measurements was limited to about −75 kHz due to thelimitations of the measurement coil.

The spectrum obtained from the measurements described above is shown inFIG. 12. The magnetic resonance structures induced a well-definedfrequency shift of the deuterium protons of about −50 KHz. Thisfrequency shift spectrum is in good agreement with estimated theoreticalvalues.

The results of this experiment demonstrated the ability of the magneticresonance structures to frequency-shift deuterium oxide protons as wellas water protons.

Example 4 Effect of Pulse Delay on Frequency Shifting by Dual-DiskMagnetic Resonance Structures

To assess the effect of the timing of preparatory off-resonance pulseson the frequency shifting of water protons and other NMR-susceptiblenuclei by magnetic resonance structures during magnetic resonancescanning measurements, the following experiment was conducted.

A grid of dual-disk magnetic resonance structures similar to thosedescribed in Example 3 were submerged in water instead of deuteriumoxide (D₂O) in a manner similar to that described in Example 3. In thisexperiment, the disks in the dual-disk magnetic resonant structures hada diameter of about 5 μm, a disk thickness of about 65 nm, and aseparation distance of about 2 μm between the disks.

The submerged grid of particles was subjected to magnetic resonancemeasurements using an indirect detection technique. The magneticresonance device delivered a series of off-resonance pulses (Gaussianshape, 100 μs in length) for a period of a few T₁'s, followed by anon-resonance 90-degree pulse, then the collection of fid data. Eachpoint in a z-spectra was calculated by integrating the fid data for eachdifferent off-resonance frequency of the preparatory pulse train. Thegap between each pulse in a preparatory pulse train was varied between 1ms and 5 ms.

The z-spectra obtained for pulse train gaps of 1 ms, 2 ms, and 5 ms areshown in FIG. 13. Closer spacing of the preparatory pulses resulted in ahigher magnitude of signal at the shifted frequency, with negligibleeffect on the amount of frequency shift.

The results of this experiment determined that that the frequency shiftinduced by the magnetic resonance structures is insensitive to thespacing of the off-resonance preparatory pulses. However, the amount offrequency-shifted water protons and other NMR-susceptible nuclei, asindicated by the magnitude of the fid signal at the shifted frequency,increases when the preparatory pulses are spaced closer together.

Example 5 Example 5: Effect of Applied Magnetic Field Strength onFrequency Shifting by Dual-Disk Magnetic Resonance Structures

To determine the effect of the applied magnetic field strength on thefrequency shifting of water protons and other NMR-susceptible nuclei bymagnetic resonance structures during magnetic resonance scanningmeasurements, the following experiment was conducted. The grid ofdual-disk magnetic resonance structures submerged in water described inExample 4 was measured using a similar indirect detection technique. Inthis experiment, an identical preparatory pulse sequence was used foreach set of measurement. However, the sets of measurements obtained inthis experiment were conducted using magnetic field strengths B₀ of 4.7T, 7.0 T, and 11.7 T. Differing magnetic field profiles from thedifferent coils used may have introduced limited variability in theresults.

The z-spectra for the fid signals induced by the magnetic resonancestructures are shown in FIG. 14. Variation in the applied magnetic fieldstrength did not significantly alter the frequency shift induced by themagnetic resonance structures. At the shift frequency, the fid signalwas higher in magnitude at the higher applied magnetic field strengths.

Example 6 Effect of Disk Radius on Frequency Shifting by Dual-DiskMagnetic Resonance Structures

To assess the sensitivity of the frequency shift induced by a dual-diskmagnetic resonance structure to variation in the radii of the disks, thefollowing experiment was conducted. Two grids of dual-disk magneticresonance structures submerged in water similar to the grid described inExample 4 were measured using a similar indirect detection technique. Inone grid, the disk diameter was about 5 μm, the thickness of each diskwas about 50 nm, and the disk separation distance was about 2 μm. In theother grid, the disk diameter was about 3 μm, the thickness of each diskwas about 50 nm, and the disk separation distance was about 1 μm.

The z-spectra obtained from the two grids of magnetic resonancestructures is shown in FIG. 15. The grid containing the smaller-radiusdual disk magnetic resonance structures had a higher frequency shiftcompared to the larger-radius grid. The frequency shifts of the twomagnetic resonance particles measured in this experiment weresufficiently separated in frequency shift (about −370 kHz vs. about −200kHz), and possessed sufficiently narrow line width to ensure thedetection of individual signals in a multiplexed magnetic resonancemeasurement technique.

The results of this experiment demonstrated that variation in the radiiof the disks in a dual-disk magnetic resonance structure resulted indetectably distinct frequency-shifting by the magnetic resonancestructures in a multiplexed magnetic resonance measurement environment.

Example 7 Effect of Disk Thickness on Frequency Shifting by Dual-DiskMagnetic Resonance Structures

To assess the sensitivity of the frequency shift induced by a dual-diskmagnetic resonance structure to variation in the thickness of the disks,the following experiment was conducted. Grids of dual-disk magneticresonance structures submerged in water similar to the grid described inExample 4 were measured using a similar indirect detection technique.Each grid contained an array of dual disk magnetic resonance structureswith the same specified disk thickness; the specified disk thickness ofthe different grids varied between about 50 nm to about 75 nm.

FIG. 16 is a summary of the z-spectrum values measured for each of thegrids having disks with varying thicknesses. Each row in FIG. 16 showsthe experimental H₂O z-spectrum for a different particle disc thickness.In this figure, the raw z-spectra of the shifted peaks atop theunshifted broadened water background is shown. This background may beeliminated by calculating the differences between correspondingpositive- and negative-frequency saturation signals to eliminate theeffects of the water background signal.

As shown in FIG. 16, the dual-disk magnetic resonance structures induceda frequency shift of about −360 kHz at a disk thickness of 50 nm, whichincreased gradually to a frequency shift of about −500 kHz at a diskthickness of 75 nm. In addition, as the thickness of the disksdecreased, the line width of the frequency shift became increasinglybroad.

The results of this experiment demonstrated that the magnitude of thefrequency shift induced by a dual-disk magnetic resonance structure maybe predictably and controllably manipulated by varying the thickness ofthe disks.

Example 8 Effect of Asymmetries of Dual-Disk Magnetic ResonanceStructures on Induced Frequency Shifting

To assess the effects of asymmetries within a dual-disk magneticresonance structure on the frequency shift induced by the structure, thefollowing simulations were conducted. Numerical calculations wereperformed to estimate the effect of various asymmetrical variations inthe geometry of a dual-disk magnetic resonance structure on thestructure's frequency shift characteristics. All calculations wereperformed for a dual disk structure having a saturated magnetic densityof 0.6 T (corresponding to nickel), a disk diameter of 2 μm, a diskthickness of 40 nm, and a disk separation distance of 0.85 μm.

One set of calculations varied the radius of one disk of the pair from100% to 65% of the value of the other disk. The results of thesecalculations are summarized in FIG. 32. As the disks become increasinglydifferent in size, there is a significant signal loss, peak broadening,and alteration of the induced frequency shift.

In another set of calculations, the thickness of the mismatched disks ina dual-disk structure was varied to determine whether the mismatch insize could be compensated for by variation in disk thickness. FIG. 33summarizes the results of these calculations, showing the z-spectrumfrom FIG. 32 for the dual-disk magnetic structure with identical disks(1.00), with one disk having a radius that was 85% of another (0.85),and with one disk that was 85% of the other, but the smaller disk isalso thinner than the larger disk to compensate for the radiusasymmetry. As shown in FIG. 33, variation in disk thickness may be usedto partially compensate for difference in disk radius.

Another set of calculations varied the offset of the centerlines of twoidentically-sized disks in a dual disk magnetic resonance structure byas much as 35% of the disk radius. FIG. 34 is a set of z-spectra forvarious centerline offsets in a direction perpendicular to theorientation of the applied magnetic field. FIG. 35 is a set of z-spectrafor various centerline offsets in a direction parallel to theorientation of the applied magnetic field. In both FIG. 34 and FIG. 35,as the centerlines of the disks are increasingly offset, there is asignificant signal loss and peak broadening.

Yet another set of calculations, the effects of cross-wafer processingvariations on the frequency-shift characteristics of the dual-diskmagnetic resonance structures were assessed. In this set ofcalculations, the effects of up to 10% interparticle variation due torandom variation in the manufacturing process was estimated. FIG. 36 isa set of z-spectra calculated assuming arrays of structures with varyingdegrees of random variation in the manufacturing process. As thevariation of the manufacturing process increases past about 1%, therewas significant signal loss.

The results of this experiment demonstrated that both systematicasymmetries, and random manufacturing errors of sufficient magnitude maysignificantly impact the efficacy of the dual-disk magnetic resonancestructure through signal loss, which impacts the detectability of thestructures, and peak broadening, which impacts the ability todiscriminate between structures with different geometries used inmultiplexed magnetic resonance visualization techniques. Thisdemonstrate the requirement of accurate microfabrication of thesestructures and precludes less accurate chemical synthesis approaches.

Example 9 Deactivation of Dual-Disk Magnetic Resonance Structures byObstruction of Reserved Volume

To demonstrate the effect of filling in the reserved space between thedisks of a dual-disk magnetic resonance structure, the followingexperiment was conducted. A grid of dual-disk magnetic resonancestructures submerged in water similar to the grid described in Example 4were measured using a similar indirect detection technique. In thisexperiment, the spaces between the disks of a portion of the structureswere filled in, as shown in SEM image in the left-hand inset of FIG. 17.The right-hand inset figure of FIG. 17 is a picture of an image obtainedby an magnetic resonance device using an indirect detection technique.The group of structures with filled-in reserved volumes (“OFF” group)did not generate a signal, and the group of structures which had openreserved volumes (“ON” group) to allow the diffusion of fluid in and outof the reserved volume generated distinct magnetic resonance signals.

The results of the experiment demonstrated that the dual-disk magneticresonance structures may be deactivated by filling in the reservedvolume, and that the signal generated by the structures was dependent onthe diffusion of fluid into the reserved volume between the disks of adual-disk magnetic resonance structure.

Example 10 Effect of Non-Uniform Cylinder Wall Thickness on FrequencyShifts of Hollow Cylinder MRS

To assess the effect of variations in the thickness of the walls of asingle hollow cylinder magnetic resonance structure, the followingsimulation was conducted. Rather than dual-disk structures, the magneticresonance structures were hollow cylinders having increasinglynon-uniformity in the cylinder wall thickness. FIG. 19B is a series ofsimulated z-spectra summarizing the results, showing diminished signalstrength and peak broadening for the hollow cylinders with non-uniformwall thickness.

The results of this experiment demonstrated that the signal strength andline width of a hollow cylinder magnetic resonance structure isrelatively sensitive to variations from a uniform wall thickness overthe full length of hollow cylinder.

Example 11 Effect of Cylinder Geometry Variation on Frequency Shifts ofHollow Cylinder MRS

To assess the effects of variations in the geometry of a hollow cylindermagnetic resonance structure on the frequency shift characteristics ofthe structure, the following simulations were conducted. Grids similarto those described in Example 10, but for the use of hollow cylindermagnetic resonance structures rather than dual-disk structures, weremeasured using an indirect detection technique. Z-spectra were obtainedusing an 11.7 T MRI scanner for four different arrays of hollow cylindergeometries. All hollow cylinders were constructed of nickel, an had anaspect ratio (length/diameter) of about 1.2.

FIGS. 23A-23D show experimental z-spectra acquired from the fourdifferent arrays of hollow cylinder magnetic resonance structures. Thehollow cylinders measured in FIG. 23A had an outer diameter of about 2μm and a wall thickness of about 75 nm. The hollow cylinders measured inFIG. 23B had an outer diameter of about 2 μm and a wall thickness ofabout 150 nm. The hollow cylinders measured in FIG. 23C had an outerdiameter of about 850 nm and a wall thickness of about 40 nm. The hollowcylinders measured in FIG. 23D had an outer diameter of about 900 nm anda wall thickness of about 50 nm.

Comparing the z-spectra of FIGS. 23A-23D, increasing the wall thicknessincreased the magnitude of the frequency shift when comparing hollowcylinders of approximately the same outer diameter. However, themagnitude of the frequency shift was dependent on a combination of allof the factors included in Equation 8 above. For example, the magnitudeof the frequency shifts for the smaller diameter cylinders, as shown inFIGS. 23C and 23D fall in between the frequency shift magnitudes of thelarger hollow cylinders, shown in FIGS. 23A and 23B. In all cases, thefrequency shifts of the hollow cylinders fell within about 10% of thefrequency shifts predicted by Equation 8 above.

The results of this experiment demonstrated the magnitudes of frequencyshifts induced by hollow cylinder magnetic resonance structures for avariety of geometries were in agreement with theoretical valuespredicted by Equation 8 above. By varying the geometries of the hollowcylinders, a multitude of distinct signals may be generated for use in amultiplexed magnetic resonance visualization technique.

Example 12 Flow Tagging Using Hollow Cylindrical MRS

To demonstrate the feasibility of flow tagging using a hollowcylindrical magnetic resonance structure, the following experiment wasconducted. Flow tagging is defined in this context as the process offrequency-shifting a plurality of water protons and otherNMR-susceptible nuclei in a moving stream, rendering thefrequency-shifted water protons and other NMR-susceptible nuclei in theflow detectable using a magnetic resonance scanner as the flow travelsthrough a flow path. In this example, a large hollow cylinder magneticresonance structure was formed by wrapping a layer of nickel around theentire circumference of a region of a tube. Two tubes were tested inwhich one tube was wrapped to a thickness of 50 μm and the and the othertube to a thickness of about 100 μm.

Water was passed through each of the two tubes at a flow velocity ofabout 0.5 m/s and about 1 m/s respectively, as shown in FIG. 27. As thewater passed through the nickel hollow cylinders wrapped around eachtube, the water protons in each pipe were periodically spin-labeled by auniform magnetic field inside each hollow cylinder, together withexposure to a RF magnetic pulse at the offset Larmor frequency, definedby the above-mentioned uniform magnetic field. The spin-labeled waterprotons produced a lower fid signal within the flow of water through themagnetic resonance imaging region downstream of each hollow cylindermagnetic resonance structure. In this experiment, the RF magnetic pulseswere applied to both tubes simultaneously.

FIG. 28 is an MRI image formed after water passing through the hollowcylinder was spin-labeled using three temporally separated RF pulses tothe hollow cylinder of the left tube, which contained water flowing atabout 0.5 m/s. The image of the left tube in FIG. 28 exhibited acharacteristic parabolic laminar flow profile from the three groups ofspin-labeled flow. A similar result was obtained for the tube with aflow velocity of about 1.0 m/s as shown in FIG. 29. In FIG. 29, thethree layers of spin-tagged flow are more spatially dispersed along thedirection of the flow due to the higher flow velocity. The distinctfrequency shifts induced by the two hollow cylinder thicknesses used inthis experiment was demonstrated by the observation that thespin-labeling of the flow in one tube did not affect the spin-labelingin the other tube. As a result, each tube may be spin-tagged separately.

To demonstrate the capability of the spin-labeling technique describedabove to perform perfusion imaging, the flow tubes described above werespin-labeled using RF labeling pulses spaced closely enough in time soas to appear continuous in subsequent MRI images. FIGS. 30 and 31 areMRI images taken from the left and right tubes, respectively. In FIG.30, the flow labeled by a rapid series of RF pulses appears as a solidcontinuous band having the same laminar parabolic flow profile as inFIG. 28. In the more rapid flow shown in FIG. 31, a similar paraboliccontinuous band was detected in the MRI image.

The results of this experiment demonstrated that the flow through tubesmay be tagged in a local region by spin-labeling the flow using a hollowcylinder magnetic resonance structure situated around the circumferenceof the tube and excitatory RF pulses. The RF pulses may be discretelyspaced in order to obtain information about finer features of the flowstructure such as parabolic flow profile, or the RF pulses may beclosely spaced to produce an essentially continuous region of taggedflow for other flow visualizations such as perfusion imaging.

Example 13 Theoretical Single-Voxel Signal Due to Transverse Dephasingfor Design of Solid Particulate MRS

To assess the effects of various factors such as the materials used toconstruct a solid particulate MRS, and the position of a solidparticulate MRS within a voxel volume on the contrast signal producedduring magnetic resonance visualization, the following experiment wasconducted. A theoretical simulation of the magnetic resonance contrastwas performed using solutions to the equations described below.

The signal intensities of the solid particulate MRS were modeledtheoretically assuming that the contrast signals originated fromindividual, micrometer-sized contrast particles with high magneticmoments and that the signals were measured using high-resolutionimaging. The calculations were simplified by assuming that the MRS fellwithin a static dephasing regime in which Δω·τ_(c)>>1, where Δω was thelocal precession frequency due to the magnetic field of the MRS, andτ_(c) was the time to diffuse a distance equal to the size of the MRS.Ignoring k-space shifting effects, the time-dependent modification tothe magnetic resonance signal S caused by the solid particulate MRS wasproportional to an integral taken over all processing spins within thevolume of interest as expressed in Eqn. (10):S(t)∝∫ρ({right arrow over (r)})·e ^(−iϕ({right arrow over (r)},t))d{right arrow over (r)}  (10)

where t was the time following excitation by an initial π/2electromagnetic pulse, {right arrow over (r)} was the spin locationrelative to the MRS, ρ was the spin density, and φ was the additionalaccrued transverse phase due to the particle field in the rotatingframe.

Since the MRS size was always far less than the voxel size in thisexperiment, the signal produced by the MRS was dominated by spins fromthe far-field region of the MRS. As a result, the magnetic field inducedby the MRS was modeled as a magnetic dipole independently of the shapeof the MRS. The MRS was assumed to be a sphere of radius determined byits net dipole moment p_(m) and the magnetic saturation of itsconstituent material. For a B₀-field aligned in the z-direction, thez-component of the field produced by the MRS when magnetized by B₀ wasB_(z)=p_(m)·(μ₀/4π)(3 cos²θ−1)/|{right arrow over (r)}|³ for a magneticpermeability to μ₀=4π·10⁻⁷ H/m and a polar angle θ. For a ferromagneticor superparamagnetic particle having a radius a and saturation magneticpolarization J_(s), the dipole moment is p_(m)=(J_(s)/μ₀)·4πa³/3,resulting in an equatorial precession frequency of Δω=γJ_(s)/3 for thegyromagnetic ratio γ.

Neither B₀ nor the magnetic susceptibility difference Δχ affects theequatorial precession frequency, since ferromagnetic andsuperparamagnetic substances are magnetized to saturation by typical B₀fields. The normalized signal decay from such a particle centered in aspherical voxel of radius R and of homogeneous spin density may then beexpressed:

$\begin{matrix}{{\frac{S(t)}{S(0)} = {\frac{3}{2( {R^{3} - a^{3}} )}{\int_{0}^{\pi}{\int_{a}^{R}{{{\exp\lbrack {{- i}\;\Delta\;{\omega \cdot t \cdot \frac{a^{3}}{r^{3}}}( {{3\;\cos^{2}\;\theta} - 1} )} \rbrack} \cdot r^{2}}\sin\;\theta\;{drd}\;\theta}}}}}\ } & (11)\end{matrix}$

Although the high magnetic moments typical of the MRS to be modeledprecluded immediate expansion of the integrand in Eqn. (11),simplification was still possible if the ratio of voxel to particleradius ((Δω)(t)(a/R)³) was on the order of unity or less. Formillisecond timescales and micrometer-sized ferromagnetic particles,this condition was fulfilled at magnetic resonance resolutions of aboutone hundred micrometers or larger. By integrating first, and thensimplifying the resultant functions of Δω(t) and Δω(t) (a/R)³ throughasymptotic and power series expansions, respectively, the signalmagnitude was approximated to second order in Δω(t)(a/R)³:

$\begin{matrix}{\frac{S(t)}{S(0)} \approx {1 - {c_{1}( {\Delta\;{\omega \cdot t \cdot \frac{a^{3}}{r^{3}}}} )} + {c_{1}( {\Delta\;{\omega \cdot t \cdot \frac{a^{3}}{r^{3}}}} )}^{2} + {{higher}\mspace{14mu}{order}\mspace{14mu}{terms}}}} & (12)\end{matrix}$

$c_{1} = {{\frac{2\pi}{3\sqrt{3}}\mspace{14mu}{and}\mspace{14mu} c_{2}} = {\frac{2}{5} + {\frac{2}{9}\lbrack {1 - \frac{\ln( {2 + \sqrt{3}} )}{\sqrt{3}}} \rbrack}^{2}}}$

The quadratic term in Eqn. (12) represented the onset of signalsaturation due to finite voxel size. Despite the limited expansion ofterms, Eqn. (12) accurately approximated the solution for the integralin Eqn. (11) for initial signal decay and saturation. Comparing thelinear and quadratic terms in Eqn. (12) estimated the dephasing period(t_(sat)) required to appreciably saturate out the voxel signal.Although the asymptotic nature of signal saturation made the definitionof the dephasing period somewhat arbitrary, as a first measure the pointat which S(t) became stationary, as approximated by Eqn (12) was used toestimate the dephasing period:

$\begin{matrix}{t_{sat} = {{{\frac{1}{\Delta\;\omega} \cdot \frac{c_{1}}{2\; c_{2}}}( \frac{R}{a} )^{3}} \approx {\frac{4}{J_{s}}( \frac{R}{a} )^{3}}}} & (13)\end{matrix}$

Although the equations developed above assumed spherical voxels, theequations were adapted to cubic voxels shapes by replacing the sphericalvoxel radius R with an effective cubic “radius” R_(c) according to therelation (4/3)πR_(c) ³=8R³, where R is the half-width of a cubic voxel.

Theoretical voxel intensities induced by a 1-μm diameter spherical MRSparticle with a J_(s)=1 T was estimated using the equations and methodsdescribed above.

FIG. 43 is a graph summarizing theoretical single-voxel signalintensities relative to background signal intensity due to transversedephasing effects of a solid particulate MRS centered within a sphericalvoxel having a diameter of 50-μm, 100-μm, or 200-μm. FIG. 44 is asimilar graph summarizing theoretical single-voxel signal intensitieswithin cubic voxels. For both FIGS. 43 and 44, as the echo time TEincreased, the contrast increased until a saturated contrast level wasreached. This saturation contrast was highest for the smallest voxelsize in both spherical and cubic voxels.

The results of this experiment demonstrated that the solid particulateMRS produced suitable signal contrast for gradient-echo MRIvisualization, particularly at the smaller voxel size of 50-100 μm.

Example 14 Theoretical Single-Voxel Signals with and without ImageDistortion Correction

To assess the effects of image distortion on the contrast signalproduced during magnetic resonance visualization, the followingsimulation was conducted. Although the image darkening produced by acontrast particle is typically dominated by T₂* transverse dephasing,for magnetic resonance conditions such as high-resolution imaging andshort echo times, geometric image distortion may also appreciably modifythe contrast signal intensity. The image distortions result from thesuperposition of the contrast particle's field onto the read magneticfield gradient, resulting in local hypointense and hyperintense contrastsignal regions near the contrast particle. If the hypointense andhyperintense contrast signal regions fall within the same voxel,conservation of spin number ensures that the spatial variations inapparent spin density cancel out within the voxel, resulting innegligible image distortion effects. However, if hypointense andhyperintense contrast signal regions fall across two or more voxels, asmay be the case for high-resolution magnetic resonance visualization,then image distortion may appreciatively change the voxel signalintensities.

To approximate the length scale of the image distortion effects,higher-order slice selection effects were ignored and 3D imaging with aread gradient of strength G in the x-direction was assumed. The field ofthe solid particulate MRS during read-out was therefore G_(x)+B_(z) ifthe B₀ offset is ignored. Spins located at a position x map to anapparent position (x+B_(z)/G), and hyperintense and hypointense signalmaxima result when |∂B_(z)/∂x| takes on a minimum or maximum value,respectively. Simplifying the analysis by setting y=z=0, setting∂B_(z)/∂x=0 gave x=−(J_(s)a³/G)^(1/4) and an associated hypointensesignal maximum mapped a distance d away from the solid particulate MRSgiven by:

$\begin{matrix}{d = {\frac{4}{3}\sqrt[4]{\frac{J_{s}a^{3}}{G}}}} & (14)\end{matrix}$

With a compensating hyperintense signal maxima similarly displaced awayfrom the solid particulate MRS, the ratio of d to the voxel sizepredicted whether image distortion significantly modified the initialsignal magnitude. Although distortion was also affected by whether B₀was parallel or perpendicular to the image plane, the distance d wasunchanged, thus the overall distortion sizes did not depend strongly onthe direction of B₀. Even with high magnetic moment MRS, imagedistortion was significant only for high-resolution imaging because dscaled as the fourth root of the magnetic dipole moment in Eqn. (14).However, for modeling the detection of single particles, high-resolutionimaging was taken into consideration. For example, substituting a 1-μmdiameter, J_(s)=1 T particle and a typical high-resolution imaginggradient G of a few Gauss/cm Eqn. (14) indicated that image distortionmay contribute to signal strength at voxel sizes of about one hundredmicrometers or less.

For solid particulate MRS with high magnetic moments and high-resolutionimaging, therefore, distortion may dominate the signal in the first fewmilliseconds following the initial excitation, after which the signalmagnitude may be dominated by dephasing effects described by Eqn. (11)above, which was assumed valid until the voxel signal started toappreciably saturate around the voxel signal saturation time t_(sat)defined by Eqn. (13). In order to capture dephasing, distortion, andsaturation effects simultaneously, the gradient-echo imaging ofindividual magnetic particles of various moments and at various imageresolutions and echo times were simulated. The simulation model trackedthe phases of a volume of spins precessing in the magnetic fieldsurrounding a magnetic dipole, with intravoxel dephasing capturedthrough a grid spacing many times smaller than the simulated voxel size.The apparent image location of each spin was determined by the netmagnetic field at that spin's real location, given by the sum of theperturbing dipole field and a simulated readout gradient.

FIG. 45 is a graph summarizing theoretical single voxel signal strengthfrom a solid particulate MRS as a function of echo time TE calculatedfor cubic voxel sizes of 50-μm, 100-μm, and 200-μm. The solid linessummarize the solutions obtained for theoretical voxel signal strengthsfor numerical simulations that included both transverse dephasing andimage distortion, and the dashed lines summarize the results obtainedfor transverse dephasing effects only. At the larger voxel size of200-μm, image distortion had a negligible effect on signal strength.However, as the voxel size and/or the echo time TE decreased, imagedistortion effects became increasingly pronounced. For example imagedistortion effects reduced the voxel signal strength by about 50% as theecho time approached zero for the 50-μm voxel size. The resultsdemonstrate that image distortion must be taken in account.

Example 15 Image Simulation with Solid Particulate MRS

To compare the effects of magnetic materials used to construct solidparticulate MRS, the echo times and the voxel resolution on the contrastsignal generated by solid particulate MRS, the following experiment wasconducted. Simulated magnetic resonance images were modeled using themethods described in Examples 14 and 15 using three different contrastparticle geometries and compositions. As a reference, acommercially-available micrometer-sized iron oxide particle (MPIO, BangsLaboratories) was modeled as a 1.63-μm diameter beads composed of 42.5%magnetite by weight and having a total magnetite content of 1.5 μg.Representative microfabricated disks were modeled as disks of purenickel and iron having a diameter of 2-μm and a thickness of 300-nm.Both microfabricated disks were surrounded by 50 to 100-nm thick shells.All particles had roughly comparable total volumes. The magnetite,nickel, and iron materials had J_(s) values of approximately 0.5 T, 0.6T, and 2.2 T, respectively. As a result, the respective magnetic dipolemoments of these particles were approximately 0.1×10⁻¹² A·m², 0.45×10⁻¹²A·m², and 1.65×10⁻¹² A·m². All particles were assumed to be centeredwithin the image voxel. The characteristics of the three contrast agentparticles are summarized in Table 1 below:

TABLE 1 Contrast Agent Material Properties Magnetic Coating Js ofMagnetic Type of Diameter Thickness material thickness magnetic dipolemoment Contrast Agent (μm) (nm) purity (% wt) and material material (T)(A · m²) MPIO sphere 1.63 — 42.5 — 0.5 0.10 · 10⁻¹² nickel disk 2 300100 Gold, 0.6 0.45 · 10⁻¹² 50-100 nm iron disk 2 300 100 Gold, 2.2 1.65· 10⁻¹² 50-100 nm

FIG. 46A-46D summarizes the results of the magnetic resonance imagesimulations. The imaging simulations for the MPIO, nickel, and ironparticles captured image darkening over several voxels rather than inonly the central voxel as previously predicted in Examples 13 and 14.For each particle, the images show theoretical (noise-free) pixelizedgradient-echo signals for various echo times from individual particlesat 50 and at 100 micrometer (cubic) isotropic resolution and for B₀oriented in-plane and perpendicular to the imaging plane. As expected,image distortion modifies the images of the nickel and iron particlesignals initially, before dephasing effects begin to dominate at higherecho times.

The results of this experiment demonstrated that the micromachined solidparticulate MRS generated higher contrast signals than a similarly-sizedexisting MPIO contrast particle.

Example 16 Effect of Off-Center Placement of Microfabricated SolidParticulate MRS in Voxels During Gradient-Echo MRI on Signal Strength

To assess the effects of the location of a contrast particle within avoxel during echo-gradient MRI on the image darkening produced by thecontrast particle, the following simulation was conducted. Althoughfractional voxel offsets have little impact at those resolutions whereimage darkening extends over many voxels such as in higher resolutionmagnetic resonance visualization performed using relatively very smallvoxel sizes, signal hypointensities drop substantially due to increasedsignal dilution arising from partial volume effects in lower resolutionmagnetic resonance visualization. For particles aligned in the middle ofan imaging slice, therefore, identical particles may appear differentlydepending on their lateral registration with regard to their respectiveimaging voxels.

Simulated magnetic resonance images were calculated for the threedifferent particles described in Example 15 in a similar manner.However, in addition to generating an magnetic resonance image assumingthat the particle was centered within its imaging voxel, threeadditional locations of the particle within the voxel were calculated.The four locations are illustrated in FIG. 47 and marked as A(centered), B (centered on right edge of voxel), C (centered on top edgeof voxel), and D (corner of voxel). All simulated magnetic resonanceimages were calculated assuming 100-μm voxel resolution and a 10 ms echotime.

FIG. 47 summarizes the magnetic resonance images calculated for thethree different contrast agents described in Example 15. For each of thecontrast agents, position-dependent signal dilution was observed. Signalhypointensity decreased as dephasing effects were averaged over anincreasing number of voxels, and decreased most severely when theparticle was located at the corner of a voxel, where the dephasingeffects may be averaged over as many as eight voxels inthree-dimensional imaging. The position-dependent signal dilutionrendered the MPIO contrast particle invisible when the particle waslocated at a voxel corner (position D in FIG. 47).

Overall signal hypointensity ranges were approximated using thesimulated magnetic resonance images because the echo time used wasselected such that image distortion and the saturation of surroundingvoxels was negligible. For example, in moving from a central point (A)to a corner point (D), signal hypointensity drops nearly four-fold intwo-dimensional imaging. Similarly, in three dimensional imaging anoffset from voxel center to corner reduces signal hypointensity as muchas eight-fold.

The results of this experiment demonstrated that the strength of thesignal of a contrast particle during magnetic resonance visualization issensitive to the position of the contrast particle within the imagingvoxel. Further, in order to enhance the visibility of the contrastparticle at arbitrary placement within the voxels during magneticresonance visualization, high magnetic moment contrast particles such asthe nickel or iron disks may be preferred.

Example 17 Comparison of Experimental MRI Images of Solid ParticulateMRS Vs. MPIO

To compare the visibility of solid particulate MRS contrast agents toexisting iron oxide micro-particles (MPIO), the following experiment wasconducted. Contrast particles similar to those described in Example 15were suspended in three separate agarose samples and subjected toT₂*-weighted, 12 ms TE, gradient-echo MRI at 50-μm and 100-μm isotropicresolution.

FIGS. 48A-48F are representative MRI images obtained for the threedifferent contrast particles. The top row of images (FIGS. 48A-48C) isimages taken at a 50-μm isotropic resolution, and the bottom row (FIGS.48D-48F) are images taken at a 100-μm isotropic resolution. The leftcolumn (FIGS. 48A and 48D) are images of the MPIO contrast particles,the center column (FIGS. 48B and 48E) are images of the nickel disks,and the right column (FIGS. 48C and 48F) are images of the iron disks,all described previously in Example 15.

As expected, higher magnetic moment particles caused more pronouncedimage darkenings. Localized hypointense regions in all images wereassumed to be primarily due to single particles due to the low particleconcentrations used and by the good agreement, at least for themicrofabricated particles, between the calculated and experimentallymeasured signal intensities.

To quantitatively compare the calculated and experimentally measuredsignal intensities, all 100-micrometer resolution image slices includingthose shown in FIG. 48 were analyzed using image analysis software thatautomatically selected and recorded the pixel intensity of all localizeddark regions in each image. The data were collected into histograms ofnormalized signal intensities (S(TE)/S(0)) approximated from the imagesby taking the ratio of signal intensity of the darkest voxels in eachdarkened region to the signal intensity averaged from a particle-freeregion of the sample image. For comparison, the experimental intensitydistributions integrated the signal intensity over variations inparticle magnetic moment, particle registration with respect to lateralvoxel position and image slice height, and background noise.

FIGS. 49A-49C are histograms summarizing the simulated andexperimentally measured signal intensities of the iron disks, nickeldisks, and MPIO contrast particles, respectively. For all contrastparticles, the simulated and the experimental histograms showedhypointensity distributions that were non-Gaussian and too broad to beexplained by background noise alone. Instead, the histograms indicatedthat the contrast signals were dominated by subvoxel-level variation inthe particle location.

The results of this experiment indicated that the experimentallymeasured magnetic resonance visualization signal intensities of thecontrast particles were in good agreement with theoretically predictedsignal intensity calculations for the solid particulate MRS. Forcomparison, the experimental intensity distributions, which integratedthe signal intensity over variations in particle magnetic moment,particle registration with respect to lateral voxel position and imageslice height, and background noise, were compared to theoretical(background noise-free) calculations.

Example 18 Determination of Minimum Particle Moments to EnsureVisibility of Solid Particulate MRS

To determine the minimum particle magnetic moments necessary to assurethe visibility of the solid particulate MRS during echo-gradient MRI,the following simulation was conducted. Contrast signal intensities werecalculated for a spherical particle with a magnetic moment ranging fromabout 10⁻¹⁴ A·m² to about 10⁻¹¹ A·m² using the methods described inExample 15. At each magnetic moment, signal intensities were calculatedfor an ensemble of particles that were positioned randomly with respectto the imaging voxel locations. Simulated magnetic resonancevisualization signal intensities were calculated assuming an isotropicresolution of 50-μm and 100-μm, and echo times of 5 ms, 10 ms, and 20ms.

FIGS. 50A-50F are graphs summarizing the calculated image intensitiesfor all conditions described above. Empirical MPIO contrast signal dataare superimposed on FIGS. 50C and 50D for comparison. The lowerboundaries of the relative signal intensities are all greater than zero,but must be greater than background noise signals to be visual. Contrastparticles having magnetic moments above the 10⁻¹³ A·m² threshold arepredicted to be visible above relatively low background noise for allconditions examined. This magnetic moment threshold is slightly lowerfor higher echo times and/or higher image resolutions.

The results of this experiment predicted that contrast particles havinga magnetic moment of at least 10⁻¹³ A·m² are visible above lowbackground noise over a variety of magnetic resonance visualizationconditions.

Example 19 Super-Resolution Tracking Using Solid Particulate MRS

To demonstrate the potential use of solid particulate MRS insuper-resolution tracking, in which the sub-voxel location of a particlemay be determined, the following experiment was conducted. Solidparticulate MRS that included iron disks coated in gold, similar tothose described in Example 15 were suspended in agarose and subjected toecho-gradient MRI as described in Example 17.

A representative MRI image is shown in FIG. 51. In FIG. 51, individualsolid particulate MRS were detected within the image. In addition, dueto the consistent size and composition of the solid particulate MRS, thesignal intensity of an individual solid particulate MRS could becompared to the signal intensities of the other solid particulate MRS todetermine the location of the particle within the imaging voxels. Forexample, the darkest voxels were assumed to indicate particles centeredwithin the voxel, and the lighter or more dispersed particle signalswere assumed to be off-center. The degree of lightening and/or signaldispersion were used to narrow down the location of the particle withinthe imaging voxels using the information from the calculated imageintensities shown in FIG. 47. On FIG. 51, individual particles arecircled and labeled using a similar convention to that of FIG. 47: theletter A denotes particles centered in the imaging voxel, B and C denoteparticles on the top or side edges of a voxel, respectively, and Ddenotes a particle on a voxel corner.

The results of this experiment demonstrated that the uniform compositionand size of the solid particulate MRS enabled these contrast particlesto be used for super-resolution tracking.

The invention has been described in detail with respect to variousembodiments, and it will now be apparent from the foregoing to thoseskilled in the art that changes and modifications may be made withoutdeparting from the invention in its broader aspects, and the invention,therefore, as defined in the claims is intended to cover all suchchanges and modifications as fall within the true concept of theinvention.

The invention claimed is:
 1. A magnetic resonance contrast agentcomprising a plurality of solid disks of uniform size and magneticmoment, wherein each disk consists of a single magnetic material and acoating made of a non-magnetic material, and wherein each disk has adiameter of about 0.1 μm to about 10 μm and a thickness of 0.5 μm to 2μm.
 2. The magnetic resonance contrast agent of claim 1, wherein eachdisk has a magnetic moment from about 10⁻¹⁴ A·m² to about 10⁻¹¹ A·m². 3.The magnetic resonance contrast agent of claim 1, wherein each diskvaries in size by less than about 5% of the average size of theplurality of disks.
 4. The magnetic resonance contrast agent of claim 3,wherein each disk varies in magnetic moment by less than about 5% of theaverage magnetic moment of the plurality of disks.
 5. The magneticresonance contrast agent of claim 1, wherein the magnetic material isiron.
 6. The magnetic resonance contrast agent of claim 1, wherein thenon-magnetic material is gold or titanium.
 7. The magnetic resonancecontrast agent of claim 6, wherein the non-magnetic material is gold. 8.The magnetic resonance contrast agent of claim 1, wherein each disk hasa diameter of about 1 μm to about 2 μm.
 9. The magnetic resonancecontrast agent of claim 8, wherein the magnetic material is iron. 10.The magnetic resonance contrast agent of claim 9, wherein thenon-magnetic material is gold.
 11. A magnetic resonance contrast agentcomprising a plurality of solid disks of uniform size and magneticmoment, wherein the disks consist of iron and a coating made oftitanium, wherein each disk has a diameter of about 0.1 μm to about 10μm and a thickness of about 0.1 μm to about 10 μm.
 12. The magneticresonance contrast agent of claim 11, wherein each disk has a diameterof about 1 μm to about 2 μm and a thickness of about 0.5 μm to about 2μm.
 13. A magnetic resonance contrast agent comprising a plurality ofsolid disks of uniform size and magnetic moment, wherein each diskconsists of a single magnetic material and a coating made of anon-magnetic material, wherein each disk has a diameter of about 1 μm toabout 2 μm and a thickness of about 0.5 μm to about 2 μm, wherein themagnetic material is iron, and wherein the non-magnetic material istitanium.